Optical System for Effecting Increased Irradiance in Peripheral Area of Object

The present invention relates generally to a novel optical system, and particularly to an optical system which provides light of increased intensity in the peripheral area of an object to be illuminated so that it is particularly useful for an illumination system or a projection system applicable to exposure of printed circuit boards, integrated circuits or the like, for exposure systems applicable to contact exposure apparatus for plate making, step-and-repeat machines or the like, and for illumination systems applicable to copy machines or the like.

It is well known that a conventional relay condenser optical system such as shown in FIG. 1 has been used in an illumination system which is intended to provide uniform illumination light for an entire object area effectively. The conventional condenser optical system, referring to FIG. 1, comprises a condenser lens C and a field lens F. The condenser optical system is designed so that the real image of a light source LS, which is s placed in front of the condenser lens C, is formed adjacent to the field lens F, and the real image of an entrance pupil A of the condenser lens C is formed on an object S which is placed behind the field lens F.

The conventional condenser optical system, however, raises a serious problem, i.e. the irradiance in the peripheral area of the object is reduced, as shown in FIG. 2, in accordance with the cosine fourth law. For instance, referring to FIG. 1, the irradiance at the point of the object where the exit angle .theta. is 27 degrees relative to the optical axis is less than that at the point on the optical axis, i.e. the point where the exit angle .theta. is zero degrees.

There are several reasons, other than the above-mentioned cosine fourth law, for the occurrence of irradiance reduction in the peripheral area of the object, which will be discussed in detail later. Actually, the irradiance in the peripheral area of the object is reduced less than a value derived from the cosine fourth law. According to the simulation calculation made by applying lens data listed in Table 1 to the optical system shown in FIG. 1, it is found that the irradiance at the point where the exit angle .theta. is 27 degrees, is reduced by 50 percent in comparison with the irradiance at the center thereof.

FIG. 3 shows an irradiance distribution on the object P, which is obtained by using the optical system shown in FIG. 1, in the case where a point source is positioned on the optical axis at the distance of 50 units away from the optical system. FIG. 4 shows an irradiance distribution of the meridional ray on the object P, and FIG. 5 shows an irradiance distribution of the sagittal ray on the object P, in each of which the point source is positioned away by 14 units from the optical axis and at a distance of 50 units from the optical system. The respective vertical axis of FIGS. 3 through 5 depicts a relative irradiance, in which the irradiance of the center of the object P is regarded as 100 percent when the point source is positioned on the optical axis. On the other hand, the respective horizontal axis of FIGS. 3 through 5 depicts a position on the object P. In FIGS. 3 through 5, the position denoted by 50 units corresponds to the position on which the exit light from the optical system is impinged.

As mentioned above, the irradiance in the peripheral area of the object P is actually reduced less than a value derived from cosine fourth law. One of the reasons therefor is an aberration, because the cosine fourth law is on the premise that an optical system has no aberration, whereas an actual optical system inevitably has some aberration.

It has then conventionally been practiced that an optical system is designed so that the aberration should be eliminated as far as possible, in other words it has commonly been practiced that an optical system is designed so as to satisfy the sine condition. Thus, even in an illumination system, the optical system for use in illumination has conventionally been designed so as to satisfy the sine condition, because it has been believed to be matter of course by a person skilled in the art.

It has been found by the inventors, however, that designing an optical system so as to satisfy the sine condition causes an irradiance reduction in the peripheral area of the object to be illuminated.

Now the reasons why there is irradiance reduction in the peripheral area of the object will be discussed.

Referring to FIG. 6, which is a schematic view of an optical system, light emitted from the light source LS enters into the optical system at the entrance height h, in this case the light source LS can be regarded as being placed at an infinite distance from the optical system, because it is positioned at a far distance from the optical system in comparison with the focal length thereof. The real image of the light source LS is formed at a point I, and the light goes through an exit pupil at an exit angle .theta.. Satisfying the sine condition means that the sine of the exit angle .theta. is proportioned to the entrance height h; accordingly the relation can be expressed by the following formula (1):

where k.sub.1 is a proportional constant.

The light which entered into the optical system at the entrance height h exits therefrom to impinge upon the point Q of the object P. Then, sin .theta. can be expressed by the following formula (2): ##EQU1## where H is the distance between the point Q and the center of the object P (hereinafter referred to as illumination height), and a is the distance between the point I and the point Q.

It can then be transformed from the formulae (1) and (2), as follows: ##EQU2##

As can be understood from FIG. 6, when the incident height h is increased, the exit angle .theta. will become large, hence the illumination height H will be increased in accordance therewith, and similarly the distance a between the point I and the point Q will also be increased. In the case where the entrance height h is increased at a constant rate, the illumination height H will be rapidly increased more than the increase of the entrance height h, since the illumination height H is proportioned to the product of the distance a and the incident height h, as can be seen from the formula (3). The relationship between the incident light radius A.sub.0 around the optical axis in the entrance pupil A and the radius P.sub.0 of the illumination area of the object P, similarly to the relationship between the incident height h and the illumination height H, is that the radius P.sub.0 increases at a greater rate than the rate at which the radius A increases, from which it will be apparent that the irradiance on the object P will be reduced as it goes away from the optical axis, in comparison with that on the entrance pupil A.

Indeed in an image-formation optical system design it will be necessary to design the optical system so as to satisfy the sine condition because it is important to minimize the aberration, but in an illumination optical system design there is no need to do so. Furthermore, designing to satisfy the sine condition causes the irradiance reduction in the peripheral area of the object to be illuminated, as mentioned above.

In a conventional illumination system, it has been practiced, in order to correct the irradiance reduction in the peripheral area of the object, that a gradient filter is placed in the optical path thereof, or that the light source is placed at a sufficient distance from the object. These conventional correction methods are, however, disadvantageous in view of the fact that light quantity is considerably reduced in the entire area of the object in the former method, and that the illumination system inevitably becomes large in size in the latter.

Furthermore, it may often be required that irradiance in the peripheral area of an object is increased in comparison with that at the center thereof. For instance, in the case where an illumination apparatus when employing a projection lens is placed optically behind an original to be reproduced, an image projected on a photosensitive material will be affected by the cosine fourth law even if uniform irradiance is given throughout the original.

It is a principal object of the present invention to provide a novel optical system particularly useful for an illumination system.

It is another object to provide an optical system which provides an illumination on an object with increased irradiance in the peripheral area of the object.

It is a further object to provide an optical system adaptable for illuminating a considerably large-scaled object, e.g. 900 mm by 900 mm.

The aforementioned objects are accomplished by the present invention, with an optical system which includes a light source, an entrance pupil for receiving light from the light source, an exit pupil for passing the light received to the object, and an optical axis which extends to the light source and the object, respectively, through the optical system, wherein the relationship among an incident height h to the entrance pupil, an illumination height H on the object and a changing rate (dh/dH) of the incident height and the illumination height is defined by a function, f(H)=(h/H) (dh/dH), the optical system being designed so as to satisfy the following formula in the peripheral area of the object: f(0)<f(H), f(0) being represented by the formula: f(0)=[fa'/{(a'-f)b'}].sup.2, where a' is a distance between the light source and the primary principal point of the optical system, and b' is a distance between the real image of the light source and the object.

According to another feature of the present invention, the optical system comprises three optical units, the first optical unit including a positive lens and having a convex rear surface, the second optical unit including a positive lens and having a convex front surface, the third optical unit including either a positive or negative lens and having a convex rear surface, the optical system satisfying the following formulae:

where f is the synthesized focal point of the optical system; f.sub.F is a distance between the front surface of the first optical unit and the primary focal point of the optical system; f.sub.B is a distance between the rear surface of the third optical unit and the secondary focal point of the optical system; n.sub.1, n.sub.3 and n.sub.5 are respectively the refractive index of the first, second and third optical units; r.sub.2 and r.sub.4 are respectively the radius of curvature of the rear surfaces of the first and second optical units; and r.sub.5 and r.sub.6 are respectively the radius of curvature of the front and rear surfaces of the third optical unit.

According to a further feature of the present invention, the optical system comprises four optical units, the first optical unit including a positive lens and having a convex rear surface, the second optical unit including either a positive or negative lens and having a convex rear surface, the third optical unit including a positive lens and having a convex front surface, the fourth optical unit including a positive lens and having a convex rear surface, the synthesized focal length of both the first and second optical units being positive, the optical system satisfying the following formulae:

where f is a synthesized focal length of the optical system; f.sub.3.4 is a synthesized focal length of both the third and fourth optical units; n.sub.5 and n.sub.7 are respectively the refractive index of the third and fourth optical units; and r.sub.5 and r.sub.8 are respectively the radius of curvature of the third and fourth optical units.

Further, according to a further feature of the present invention, the optical system comprises two optical units, the first optical unit including a positive lens and having a convex rear surface, the second optical unit including a positive lens and having convex front and rear surfaces, the optical system satisfying the following formulea:

where f is a synthesized focal length of the optical system; f.sub.2 is the focal length of the second optical unit; d.sub.3 is the thickness of the second optical unit; and r.sub.4 is the radius of curvature of the rear surface of the second optical unit.

According to a further feature of the invention, the optical system comprises two optical units, the first optical unit including a positive lens and having a convex rear surface, the second optical unit including a positive lens and having a concave front surface and a convex rear surface, the optical system satisfying the following formulae:

where f is the synthesized focal length of the optical system; r.sub.2, r.sub.3 and r.sub.4 are the radius of curvature of the rear surface of the first optical unit and of the front and rear surfaces of the second optical unit, respectively; and n.sub.1 and n.sub.3 are refractive indexes of the first and second optical units.

The optical system is preferably formed into so called a fly's eye configuration.

Having the aforementioned features, the present invention has the following useful advantages:

The optical system according to the present invention effectively resolves the irradiance reduction caused by the cosine fourth law and/or vignetting in the peripheral area of an object to be illuminated.

The optical system instead increases the irradiance in the peripheral area of an object to be illuminated, which fact reveals that the optical system is particularly useful in the case where the image of the object is in turn projected onto e.g. a photosensitive material. The resultant irradiance distribution on the photosensitive material can be ensured to be uniform throughout the entire surface thereof.

The optical system according to the present invention is accordingly adaptable for illuminating a considerably large-scaled object.

Other novel features and advantages of the invention will become apparent in the course of the following detailed description taken together with the accompanying drawings, which are directed only to the understanding of the present invention and not to the restriction of the scope of the invention.

FIG. 1 is an elevational view of a conventional optical system;

FIG. 2 is a graphic representation which shows irradiance distribution of the conventional optical system;

FIGS. 3 through 5 are respectively graphic representations of the irradiance distribution on the object, when using the conventional optical system;

FIG. 6 is a schematic elevational view of the conventional optical system;

FIG. 7 is a graphic representation which shows the relationship between the entrance height and the illumination height;

FIG. 8 is a schematic view of an illumination apparatus according to the present invention;

FIG. 9 is a schematic view of an illumination apparatus according to present invention;

FIG. 10 is a side view of lenses forming the optical system;

FIGS. 11-(A) through 11-(C) are graphic representations showing an irradiance distribution on an object;

FIG. 12 is a side view of lenses forming the optical system;

FIGS. 13-(A) through 13-(C) are graphic representations showing an irradiance distribution on an object;

FIG. 14 is a side view of lenses forming the optical system;

FIGS. 15-(A) through 15-(C) are graphic representations showing an irradiance distribution on an object;

FIG. 16 is a side view of lenses forming the optical system;

FIGS. 17-(A) through 17-(C) are graphic representations showing an irradiance distribution on an object;

FIG. 18 is a side view of lenses forming the optical system;

FIGS. 19-(A) through 19-(C) are graphic representations showing an irradiance distribution on an object;

FIG. 20 is a side view of a lens forming the optical system;

FIGS. 21-(A) through 21-(C) are graphic representations showing an irradiance distribution on an object;

FIG. 22 is a side view of lenses forming the optical system;

FIGS. 23 and 24 are explanatory side views showing light rays passing through the optical system;

FIG. 25 is a graphic representation showing an irradiance distribution on an object;

FIG. 26 is a side view of lenses forming the optical system;

FIG. 27 is a graphic representation showing an irradiance distribution on an object;

FIG. 28 is a side view of lenses forming the optical system;

FIG. 29 is a graphic representation showing an irradiance distribution on an object;

FIG. 30 is a side view of lenses forming the optical system;

FIG. 31 is a graphic representation showing an irradiance distribution on an object;

FIG. 32 is a side view of lenses forming the optical system;

FIG. 33 is a graphic representation showing an irradiance distribution on an object;

FIG. 34 is a side view of lenses forming the optical system;

FIG. 35 is a graphic representation showing an irradiance distribution on an object;

FIG. 36 is a side view of lenses forming the optical system;

FIG. 37 is a graphic representation showing an irradiance distribution on an object;

FIG. 38 is a side view of lenses forming the optical system;

FIG. 39 is a graphic representation showing an irradiance distribution on an object;

FIG. 40 is a side view of a lens forming the optical system;

FIGS. 41 and 42 are explanatory side views of the light rays passing through the optical system;

FIG. 43 is a graphic representation showing an irradiance distribution on an object;

FIG. 44 is a side view of lenses forming the optical system;

FIG. 45 is a graphic representation showing an irradiance distribution on an object;

FIG. 46 is a side view of lenses forming the optical system;

FIG. 47 is a graphic representation showing an irradiance distribution on an object;

FIG. 48 is a side view of lenses forming the optical system;

FIG. 49 is a graphic representation showing an irradiance distribution on an object;

FIG. 50 is a side view of lenses forming the optical system;

FIG. 51 is a graphic representation showing an irradiance distribution on an object;

FIG. 52 is a side view of lenses forming the optical system;

FIG. 53 is a graphic representation showing an irradiance distribution on an object;

FIG. 54 is a side view of lenses forming the optical system;

FIGS. 55 and 56 are explanatory side views showing the light rays passing through the optical system;

FIG. 57 is a graphic representation showing an irradiance distribution on a object;

FIG. 58 is a side view of lenses forming the optical system;

FIG. 59 is a graphic representation showing an irradiance distribution on an object;

FIG. 60 is a side view of lenses forming the optical system;

FIG. 61 is a graphic representation showing an irradiance distribution on an object;

FIG. 62 is a side view of lenses forming the optical system;

FIG. 63 is a graphic representation showing an irradiance distribution on an object;

FIG. 64 is a side view of lenses forming the optical system;

FIG. 65 is a graphic representation showing an irradiance distribution on an object;

FIG. 66 is a side view of lenses forming the optical system;

FIG. 67 is a graphic representation showing an irradiance distribution on an object;

FIG. 68 is a side view of lenses forming the optical system;

FIGS. 69 and 70 are explanatory side views showing the light rays passing through the optical system;

FIG. 71 is a graphic representation showing an irradiance distribution on an object;

FIG. 72 is a side view of lenses forming the optical system;

FIG. 73 is a graphic representation showing an irradiance distribution on an object;

FIG. 74 is a side view of lenses forming the optical system;

FIG. 75 is a graphic representation showing an irradiance distribution on an object;

FIG. 76 is a side view of lenses forming the optical system;

FIG. 77 is a graphic representation showing an irradiance distribution on an object;

FIG. 78 is a side view of lenses forming the optical system;

FIG. 79 is a graphic representation showing an irradiance distribution on an object;

FIG. 80 is a graphic representation showing an irradiance distribution on a photosensitive material;

FIG. 81 is a schematic side view of an illumination apparatus according to the present invention;

FIG. 82 is a graphic representation showing an irradiance distribution on a photosensitive material;

FIG. 83 is a graphic representation showing a vignetting factor of a projection lens; and

FIG. 84 is a graphic representation showing an irradiance distribution on a photosensitive material.

Referring to FIG. 8, a light source LS is located on the optical axis Z, and, when the light ray b.sub.1 emitted from the center LS.sub.0 of the light source LS enters into the entrance pupil A of a lens L at the entrance height h, the light ray B.sub.1 advances through the lens L and emerges from the exit pupil B, to reach the object P at the height H.

Similarly, a light ray entering into the entrance pupil at a height h+.DELTA.h reaches the object at a height H+.DELTA.H. In this case, assuming that light intensity is not lost during the light transmission through the lens, the radiant flux transmitted through the area .DELTA.S.sub.1 between a circle of radius h and a circle of radius h+.DELTA.h reaches the area .DELTA.S.sub.2 between the circle of radius H and that of radius H+.DELTA.H. These areas .DELTA.S.sub.1 and .DELTA.S.sub.2 are represented as follows:

Assuming that the irradiance at the incident height h at the entrance pupil A is defined as e, the irradiance E at the illumination height H on the object P can be expressed as ##EQU3##

Then, assuming that .DELTA.H is brought infinitely close to zero, the following formulae are obtained: ##EQU4## The formula (6) then can be expressed as follows:

where f(H)=(dh/dH)(h/H).

In order to increase the irradiance in the peripheral area of the object, the optical system according to the present invention is designed to so as to satisfy the following formula:

In the case where the irradiance e in the entrance pupil A can be regarded as constant independent of the incident height h, in other words, in the case where the irradiance distribution in the entrance pupil A is uniform, the aforementioned function f(H) represents the relative irradiance on the object P in connection with the irradiance e.

The relative irradiance at the illumination height H=0 on the object P is represented by the function f(0), whereas the relative irradiance at the illumination height H.noteq.0 thereon is represented by the function f(H).

By the way, in the paraxial region the illumination height H can be expressed as follows:

then, the function f(0) can be expressed as follows:

where a' is the distance between the light source and the primary principal point, f is the focal length, and b' is the distance between the real image of the light source and the object.

Referring to FIG. 9, which shows a schematic view of the illumination apparatus according to the present invention, the illumination apparatus comprises a light source 1, an ellipsoidal mirror 2 provided with respect to the light source, an optical system 3, e.g. formed into a fly's eye configuration, a diffusing plate 4, an original 5 to be reproduced placed immediately behind the diffusing plate, a projection lens 6 and a photosensitive material 7, in order. The light source 1 is a mercury lamp, with respect to which the ellipsoidal mirror 2 is provided. The ellipsoidal mirror is designed that the exit terminal thereof is 170 mm in radius. The optical system 3 is placed 500 mm away from the exit terminal of the light source. Light reflected by the marginal end of the mirror 2 is at an angle of 18.8 degrees relative to the optical axis, to be received by the optical system 3. Light emerged from the optical system 3 impinges upon the diffusing plate 4, by which the light is well diffused suitable for uniform illumination of the original. The diffusing plate 4 is placed 1000 mm away from the exit terminal of the optical system 3. The original 5, e.g. a transparency, is placed immediately behind the diffusing plate. The projection lens 6 is designed so that the focal length thereof is 600 mm and it is placed 1200 mm away from the original 5. The photosensitive material 7 is placed 1200 mm away from the exit surface of the projection lens. In this case, the entire area of an original having a 900 mm diagonal is illuminated, and the image illuminated is projected on the photosensitive material at 1:1 magnification.

As mentioned above, the optical system 3 is formed into a fly's eye configuration, wherein a plurality of similar optical systems are aligned two-dimensionally. In the embodiments shown hereinafter, only one of such optical system is illustrated.

Hereinafter described are examples of the optical system 3 to be employed in the illumination apparatus shown in FIG. 9. In the following examples, the respective optical elements shown in FIG. 8 are designed as follows:

Focal length of the lens L (i.e. optical system 3 in FIG. 9) is f=1.0;

The distance between the light source LS and the optical system L (i.e. optical system 3 in FIG. 9) is a'=50; and

Size of the light source LS is 2a'tan .omega..

In the case where any surface is aspherical, such aspherical surface will be defined with both the Z-coordinate corresponding to the optical axis and the Y-coordinate corresponding to the height from the optical axis, and the value of the Z-coordinate will be represented by the following formula:

where C=1/r (r is a radius of curvature); K is a conic constant; and A.sub.1, A.sub.2, A.sub.3 and A.sub.4 are aspheric constants.

Referring to FIG. 10, which shows a side view of the lenses forming the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the second surface r.sub.2 thereof is aspherical. The lens data of this optical system are shown in Table 2.

The conic constant and aspheric constants of the second surface r.sub.2 are shown in Table 3.

In this example, the lens is so designed that the effective diameter of the entrance pupil A is 1.24, and that the effective view angle at the center of the entrance pupil A is 37.6 degrees.

FIGS. 11-(A) through 11-(C) are graphic representations showing the irradiance distribution on the object, which irradiance distribution is effected by the light rays starting from points LS.sub.0, LS.sub.1 and LS.sub.2 of the light source, respectively. The point LS.sub.0 corresponds to that on the optical axis, the point LS.sub.1 corresponds to that at the height of 70 percent of the radius of the light source, and the point LS.sub.2 corresponds to that at the upper end of the light source. In these Figures, the horizontal axis represents the height from the optical axis on the object, and the vertical axis represents the relative irradiance (%) when the irradiance at the center of the object is regarded as 100 (%).

It will be understood from these Figures that the irradiance on the object increases gradually from the center toward the peripheral area. The peripheral irradiance becomes more than 150 percent in the case where the light rays starting from the point LS.sub.0 irradiates the object (FIG. 11-(A)).

This example may be especially advantageous, since the refractive index is relatively small, hence common optical glass can be used.

FIGS. 13-(A) through 13-(C) are graphic representations showing irradiance distribution on the object, which irradiance distribution is effected by the light rays from the points LS.sub.0, LS.sub.1 and LS.sub.2 of the light source, respectively.

It will be understood from these Figures that the irradiance on the object increases gradually from the center to the peripheral area.

This example may be particularly advantageous, since the effective view angle can be relatively wide, although the optical system comprises three spherical lenses.

Referring to FIG. 14, which shows a side view of forming the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2. All the surfaces thereof are spherical, and the lens data are listed in Table 5.

FIGS. 15-(A) through 15-(C) are graphic representations showing irradiance distribution on the object, which irradiance distribution is effected by the light rays from the points LS.sub.0, LS.sub.1 and LS.sub.2 of the light source, respectively.

It will be understood from these Figures that the irradiance on the object increases gradually from the center to the peripheral area. This example may be particularly advantageous, since the optical system comprises only two spherical lenses, hence the manufacturing costs can be decreased.

Referring to FIG. 16, which shows a side view of the lenses forming the optical system the optical system comprises four optical units and four lenses L.sub.1 to L.sub.4. All the surfaces thereof are spherical, and the lens data are listed in Table 6.

FIGS. 17-(A) through 17-(B) are graphic representations showing irradiance distribution on the object, which irradiance distribution is effected by the light rays from the points LS.sub.0, LS.sub.1 and LS.sub.2 of the light source, respectively.

It will be understood from these Figures that the irradiance increases gradually from the center to the peripheral area. This example may be particularly advantageous, since all the lenses employed have low refractive indexes, and hence common optical glass can be used.

Referring to FIG. 18, which shows a side view of the lenses forming the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2. The second and third surfaces thereof are aspherical, and the lens data are listed in Tables 7 and 8.

FIGS. 19-(A) through 19-(C) are graphic representations showing the irradiance distribution on the object, which irradiance distribution is effected by the light rays from the points LS.sub.0, LS.sub.1 and LS.sub.2 of the light source, respectively.

It will be understood from these Figures that irradiance on the object increases gradually from the center to the peripheral area. This example may be particularly advantageous, since the optical system has a wide view angle, although it comprises only two lenses.

Referring to FIG. 20, which shows a side view of the lens forming the optical system 3 of this example, the optical system comprises a single optical unit including a single lens L.sub.1. All the surfaces thereof are aspherical, and the lens data are listed in Tables 9 and 10.

FIGS. 21-(A) through 21-(C) are graphic representations showing the irradiance distribution on the object, which irradiance distribution is effected by the light rays from the points LS.sub.0, LS.sub.1 and LS.sub.2 of the light source, respectively.

It will be understood from these Figures that the irradiance on the object increases gradually from the center to the peripheral area. This example may be particularly advantageous, since the optical system comprises only a single lens, and the aspherical surfaces can be manufactured through molding. This is practically advantageous for mass production thereof, since there is no need to adjust the distance between the surfaces.

According to another feature of the present invention, the optical system 3 employed in the illumination apparatus shown in FIG. 9 comprises three optical units including three lenses, the first optical unit comprising a single positive lens having a convex rear surface, the second optical unit comprising a single positive lens having a convex front surface, and the third optical unit comprising a single either positive or negative lens and having a convex rear surface, the optical system satisfying the following formulae:

where f is the synthesized focal point of the optical system as a whole; f.sub.F is the distance between the front surface of the first optical unit and the primary focal point of the optical system; f.sub.B is the distance between the rear surface of the third optical unit and the secondary focal point of the optical system; n.sub.1, n.sub.3 and n.sub.5 are respectively the refractive index of the first, second and third optical units; r.sub.2 and r.sub.4 are respectively the curvature of radius of the rear surfaces of the first and second optical unit; and r.sub.5 and r.sub.6 are respectively the curvature of radius of the front and rear surfaces of the third optical unit.

Referring to FIGS. 8 and 22 through 24, the optical system in this embodiment comprises three optical units each of which comprises a single lens. Both the distance a between the light source LS and the lens L and the distance b between the lens L and the object P are designed to be sufficiently large in comparison with the synthesized focal length f of the lenses L.sub.1, L.sub.2 and L.sub.3. The optical system is designed so that the entrance pupil A is located in the vicinity of the front surface of the first lens L.sub.1.

The optical system according to this embodiment is designed to satisfy the formula (13);

Both the front surface of the first lens and the synthesized focal point of the optical system are relatively close to each other, and accordingly the object surface P will be conjugate to the front surface of the first lens, whereby the incident rays forming an angle relative to the optical axis will effectively reach the object surface P, as shown in FIG. 24.

The optical system according to this embodiment is designed to satisfy the formula (14):

This formula (14) defines the refracting power of the surface r.sub.6 (i.e. the rear surface of the third lens), by which the exit angle .theta. of the rays Q.sub.1 incident to the optical system at the incident height h is controlled not to be excessively large.

As shown in FIG. 23, the incident rays formed into parallel rays are refracted by the lenses L.sub.1 and L.sub.2, wherein the ray entering at a large incident height is subject to large refraction due to spherical aberration. The intersection I.sub.1 where the marginal rays Q.sub.1 intersect the optical axis Z will then be located before the intersection I.sub.2 where the paraxial rays Q.sub.2 intersect the optical axis.

On the other hand, as conditioned by the formula (15), the surface r.sub.6 (i.e. the rear surface of the third lens) is located behind the intersections I.sub.1 and I.sub.2 and has a large refracting power as defined by the formula (14). The refracting power of the surface r.sub.6 will not sufficiently act on the marginal rays Q.sub.1, and the surface r.sub.6 will rather effect the divergence on the paraxial rays Q.sub.2 which enters at low incident height and intersect the optical axis behind the center of curvature C.sub.6. Consequently, the optical system minimizes the exit angle .theta. of a marginal ray which enters at a relatively high incident height h, so that the peripheral irradiance on the object is not undesirably reduced.

The optical system according to the embodiment is further designed to satisfy the formula (15):

This formula denotes that the back focal length should be designed to preferably be negative, although it may be designed to be slightly positive.

The optical system has a sufficient length to the extent that the rays starting out from a point away from the optical axis will not be vignetted, wherein the surface r.sub.6 (i.e. the rear surface of the third lens) is located behind the intersections I.sub.1 and I.sub.2, and the back focal length f.sub.B is defined within the range conditioned by the formula (15).

Furthermore, the optical system of this embodiment is designed to satisfy the formula (16):

This formula defines the refracting power of the surface r.sub.2 (i.e. the rear surface of the first lens), by which the function of the surface r.sub.6 conditioned by the formula (14) can be fulfilled effectively.

In the case where the refracting power is less than the lowest value of the formula (16), the spherical aberration is small, and hence the function of the surface r.sub.6 will not be fulfilled sufficiently. On the other hand, in the case where the refracting power is greater than the highest value of the formula (16), the incident height h of the ray Q.sub.4 starting from the lower end of the light source and entering the surface r.sub.6 will be excessively high, and hence the exit angle .theta. the ray emerging therefrom will be excessively small, accordingly the ray cannot reach the periphery of the object.

The optical system of this embodiment is further designed to satisfy the formula (17): ##EQU5## This formula requires that the sum of both the refracting power of the surface r.sub.4 and that of the surface r.sub.5 is negative.

The air lens formed between the surfaces r.sub.4 and r.sub.5 has a diverging function, by which the ray Q.sub.4 emitted from the lower end of the light source and emerging from the surface r.sub.6 is raised upward to obtain the exit angle .theta..

Hereinafter described are examples of the optical system conditioned by the formulae (13) through (17). In the following examples, the optical system L (i.e. optical system in FIG. 9) is placed a=50 away from the light source having the radius y=15, and the object P is placed b=100 away from the rear surface of the optical system.

Referring to FIG. 22, which shows a side view of the optical system 3 of this example, the optical system comprises three optical units including three lenses L.sub.1 through L.sub.3, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 11.

In the example, the optical system is designed so that the conditions defined by the formulae (13) through (17) have intermediate values.

FIG. 25 shows the irradiance distribution on the object effected by the optical system of this example, from which it can be understood that the irradiance distribution on the object is within the range of .+-.2 percent.

Referring to FIG. 26, which shows a side view of the lenses forming the optical system 3 of this example, the optical system comprises three optical units including three lenses L.sub.1 through L.sub.3, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 12.

In the example, the optical system is designed so that the conditions defined by the formulae (13) through (17) are satisfied.

FIG. 27 shows the irradiance distribution on the object effected by the optical system of this example, from which it can be understood that the irradiance distribution on the object is within the range of .+-.4 percent.

Referring to FIG. 28, which shows a side view of the optical system 3 of this example, the optical system comprises three optical units including three lenses L.sub.1 through L.sub.3, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 13.

In the example, the optical system is designed so that the conditions defined by the formulae (13) through (17) are satisfied.

FIG. 29 shows the irradiance distribution on the object effected by the optical system of this example, from which it can be understood that the irradiance distribution on the object is within the range of .+-.3 percent.

Referring to FIG. 30, which shows a side view of the optical system 3 of this example, the optical system comprises three optical units including three lenses L.sub.1 through L.sub.3, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 14.

In the example, the optical system is designed so that the conditions defined by the formulae (13) through (17) are satisfied.

FIG. 31 shows the irradiance distribution on the object effected by the optical system of this example, from which it can be understood that the irradiance distribution on the object is within the range of .+-.2 percent.

Referring to FIG. 32, which shows a side view of the optical system 3 of this example, the optical system comprises three optical units including three lenses L.sub.1 through L.sub.3, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 15.

In the example, the optical system is designed so that the conditions defined by the formulae (13) through (17) are satisfied.

FIG. 33 shows the irradiance distribution o the object effected by the optical system of this example, from which it can be understood that the irradiance distribution on the object is within the range of .+-.4 percent.

Referring to FIG. 34, which shows a side view of the optical system 3 of this example, the optical system comprises three optical units including three lenses L.sub.1 through L.sub.3, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 16.

In the example, the optical system is designed so that the conditions defined by the formulae (13) through (17) are satisfied.

FIG. 35 shows the irradiance distribution on the object effected by the optical system of this example, from which it can be understood that the irradiance in the peripheral area of the object is increased about 20 percent.

Referring to FIG. 36, which shows a side view of comprises three optical units including three lenses L.sub.1 through L.sub.3, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 17.

In the example, the optical system is designed so that the conditions defined by the formulae (13) through (17) are satisfied.

FIG. 37 shows the irradiance distribution on the object effected by the optical system of this example, from which it can be understood that the irradiance distribution on the object is within the range of .+-.5 percent.

Referring to FIG. 38, which shows a side view of the optical system 3 of this example, the optical system comprises three optical units including three lenses L.sub.1 through L.sub.3, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 18.

In the example, the optical system is designed so that the conditions defined by the formulae (13) through (17) are satisfied.

FIG. 39 shows the irradiance distribution on the object effected by the optical system of this example, from which it can be understood that the irradiance distribution on the object is within the range of .+-.5 percent.

According to the embodiment conditioned by the formulae (13) through (17), the optical system enables the irradiance within the range of 80 to 90 in diameter on the object to be approximately uniform or effectively increased in the peripheral area thereof, which range corresponds to the exit angle of 22 to 27 degrees.

In comparison with a conventional illumination apparatus, by which uniform irradiation distribution to the extent of .+-.5 percent on the object can be effected within only about 10 degrees of the exit angle, the distance between the optical system and the object can be reduced up to half to one-third when the same area is illuminated with approximately the same irradiance distribution.

According to a further feature of the present invention, the optical system 3 employed in the illumination apparatus shown in FIG. 9 comprises four optical units including four lenses, the first optical unit comprising a single positive lens and having a convex rear surface, the second optical unit comprising a single either positive or negative lens and having a convex rear surface, the third optical unit comprising a single positive lens and having a convex front surface, the fourth optical unit comprising a single positive lens and having a convex rear surface, the synthesized focal length of both the first and second lenses being positive, the optical system satisfying the following formulae:

where f is a synthesized focal length of the optical system as a whole; f.sub.3.4 is a synthesized focal length of both the third and fourth lenses; n.sub.5 and n.sub.7 are respectively the refractive index of the third and fourth lens; and r.sub.5 and r.sub.8 are respectively the radius of curvature of the third and fourth lens.

In this embodiment the first and second optical units L.sub.1 and L.sub.2 perform a part of functions of a condenser lens, since the synthesized focal length of these optical units is positive. The first optical unit comprises a single positive lens and has a convex rear surface and the second optical unit comprises a single either positive or negative lens and has a convex rear surface. These optical units will accordingly cause both the large spherical aberration and coma.

Because of the spherical aberration the intersection of both the marginal rays Q.sub.1 and the optical axis Z will be located before the intersection of both the paraxial rays Q.sub.2 and the optical axis. Because of the coma the exit angle .theta. of the marginal ray Q.sub.3 is controlled not be excessively large.

On the other hand, the third optical unit L.sub.3 comprises a single positive lens and has a convex front surface which functions as a condenser lens, whereas the fourth optical comprises a single positive lens and has a convex rear surface. These optical units in combination with each other function as a field lens and enable the peripheral irradiation of the object to be uniform or increased.

As can be seen in FIG. 41, the rear surface r.sub.8 of the fourth lens L.sub.4 is located behind the image points I.sub.1 and I.sub.2. The refracting power of the surface r.sub.8 will not effectively act on the marginal rays Q.sub.1, which enter at large incident height and intersects the optical axis at the point I.sub.1, the diverging function will rather act on the paraxial rays Q.sub.2, which enter at a small incident height and intersects the optical axis at the point I.sub.2. In other words, the lenses L.sub.3 and L.sub.4 control the exit angle .theta. of rays entering at a relatively large incident height, to avoid the irradiance reduction in the peripheral area of the object.

In order to enable the optical system to control the exit angle and to avoid the irradiance reduction in the peripheral area of the object, it will be most effective that both the front surface of the third lens and the rear surface of the fourth lens have high refracting power. For this reason, the following condition is given:

The formula (58) denotes that the irradiance reduction cannot be corrected when the right-side of the formula is smaller than 0.8.

The lenses L.sub.3 and L.sub.4 also satisfy the following condition:

The formula (59) denotes that the lenses L.sub.3 and L.sub.4 are designed to have the function of a field lens and to avoid the eclipse caused by vignetting. When the value of the synthesized focal length f.sub.3.4 is smaller than 0.75f, the refracting power acting on the marginal rays Q.sub.3, will be excessively strong, and then the exit angle will become excessively small, accordingly an effective illumination area on the object will become small.

On the contrary, when the value of the synthesized focal length f.sub.3.4 is larger than 1.52f, an image formed in the conjugate plane of the entrance pupil will become small, since the magnification is in inverse proportion to the value f.sub.3.4 due to the conjugate relationship between the entrance pupil and the image plane. Further, the refracting power of the lenses L.sub.3 and L.sub.4 will become small, and it will then be impossible to minimize, independent of the size of the light source, the exit angle of the rays entering at a large incident height, and consequently a remarkable irradiance reduction will be caused in the peripheral area of the object.

In the light of this, the formula (59) defines a preferable range of the synthesized focal length to satisfactorily achieve the correction of the irradiance reduction in the peripheral area of the object.

Hereinafter described are examples of the optical system conditioned by the formulae (58) and (59). In the following examples, the optical system L (i.e. optical system 3 in FIG. 9) is designed so that the diameter of the light source=20 (maximum incident angle .omega..sub.max =11.3 degrees); the distance between the light source and the entrance pupil=50; the distance between the rear surface of the fourth lens and the object=100; the diameter of the object=80 (maximum exit angle .theta..sub.max =21.8 degrees); the effective diameter of respective lenses=1.0; and the synthesized focal length of the optical system as a whole=1.0. The optical system is further designed so that the entrance pupil A is placed at the front surface of the first lens L.sub.1, and that the image of the entrance pupil is imaged on the object.

Referring to FIG. 40, which shows a side view of the optical system 3 of this example, the optical system comprises four optical units including four lenses L.sub.1 through L.sub.4, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 19.

FIG. 43 shows an irradiance distribution on the object, from which it will be apparent that the irradiance is increases gradually toward the the peripheral area.

Referring to FIG. 44, which shows a side view of the optical system 3 of this example, the optical system comprises four optical units including four lenses L.sub.1 through L.sub.4, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 20.

FIG. 45 shows an irradiance distribution on the object. In this example, the optical system is designed so that the maximum illumination height=97.6 in diameter (maximum exit angle: .theta..sub.max =26 degrees), and that the irradiance reduction in the intermediate area of the object is controlled to increase the irradiance in the peripheral area of the object.

Referring to FIG. 46, which shows a side view of the optical system 3 of this example, the optical system comprises four optical units including four lenses L.sub.1 through L.sub.4, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 21.

FIG. 47 shows an irradiance distribution effected on the object by this example. This example is the case where the synthesized focal length f.sub.3.4 is of the minimum value.

Referring to FIG. 48, which shows a side view of the optical system 3 of this example, the optical system comprises four optical units including four lenses L.sub.1 through L.sub.4, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 22.

FIG. 49 shows an irradiance distribution effected on the object by optical system. This example is the case where the synthesized focal length f.sub.3.4 is of the minimum value.

Referring to FIG. 50, which shows a side view of the optical system 3 of this example, the optical system comprises four optical units including four lenses L.sub.1 through L.sub.4, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 23.

FIG. 51 shows an irradiance distribution effected on the object by this example. This example is the case where the sum of both the refracting powers of the front surface of the third lens and the rear surface of the fourth lens is of the minimum value.

Referring to FIG. 52, which shows a side view of the optical system 3 of this example, the optical system comprises four optical units including four lenses L.sub.1 through L.sub.4, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 24.

FIG. 53 shows the irradiance distribution effected on the object by this example, from which it will be apparent that the irradiance is more than 93 percent throughout the object.

According to a further feature of the present invention, the optical system 3 employed in the illumination apparatus shown in FIG. 9 includes two optical units including two lenses, the first optical unit comprising a single positive lens having a convex rear surface and the second optical unit comprising a single positive lens having convex front and rear surfaces, the optical system satisfying the following formulae:

where f is a synthesized focal length of the optical system as a whole; f.sub.2 is the focal length of the second optical unit; d.sub.3 is the thickness of the second optical unit; and r.sub.4 is the radius of curvature of the rear surface of the second optical unit.

According to this embodiment, the incident rays entering into the optical system are subject to the refracting power of the rear surface of the first lens L.sub.1, and the larger the incident height of the entering ray, the more strongly the refracting power of the rear surface of the first lens acts on the same due to the spherical aberration. As shown in FIG. 55, the intersection I.sub.1 of both the marginal rays Q.sub.1 and the optical axis Z accordingly is located before the intersection I.sub.2 of both the paraxial rays Q.sub.2 and the optical axis.

The rear surface r.sub.4 of the second lens L.sub.2 locates behind the intersections I.sub.1 and I.sub.2 and has a strong refracting power. The refracting power of the surface r.sub.4 will not act on the marginal rays Q.sub.1, and the diverging function will rather act on the paraxial rays Q.sub.2. The optical system of this embodiment controls the exit angle of the rays entering at relatively large incident height, so that the irradiance reduction in the peripheral area of the object is effectively resolved.

The rear surface of the first lens L.sub.1 effects the positive coma, which implies that the rear surface r.sub.2 of the first lens L.sub.1 is defined within the range where the incident height to the rear surface r.sub.4 of the second lens L.sub.2 of a marginal ray Q.sub.3 will not become excessively large, as can be seen in FIG. 56. This is because, when the incident height to the rear surface r.sub.4 of the second lens is excessively large, the exit angle .theta. therefrom will, to the contrary, become excessively small due to the refracting power of the surface r.sub.4, and the effective illumination area will accordingly become small.

The optical system of this embodiment is designed to satisfy the formula (76):

This condition defined by the formula (76) ensures that the rays refracted by the rear surface r.sub.4 of the first lens L.sub.2 is not subject to the vignetting caused by a lens barrel and does not emerge therefrom at an excessively small exit angle.

When the value of (d.sub.3 /r.sub.4) is smaller than -3.0, the refracting power of the surface r.sub.4 will become large since the radius of curvature of the surface r.sub.4 is negative, and the exit angle of the marginal rays Q.sub.1 and Q.sub.3 will accordingly become excessively small. Consequently, the effective illumination area of the object will become small. In this case, the thickness d.sub.3 of the second lens L.sub.2 will become relatively large, and the vignetting will accordingly be caused to effect loss of light intensity.

On the other hand, when the value of (d.sub.3 /r.sub.4) is larger than -0.3, it is necessary in order to improve the refracting power of the second lens L.sub.2 that the radius of curvature r.sub.3 of the front surface thereof is small as shown by an imaginary line in FIG. 56, and that the distance d.sub.2

between the lenses is large. The marginal ray Q.sub.3 entering the lower end of the first lens will then impinge upon the front surface of the second lens at a larger incident height, and the refracting power of the front surface of the second lens will accordingly act thereon to result in an excessively small exit angle .theta., thereby the effective illumination area on the object will consequently become small.

The optical system of this embodiment is further designed to satisfy the formula (77):

When the value of the focal length f.sub.2 of the second lens L.sub.2 is smaller than 1.0f, the refracting power of the second lens will strongly act on the marginal ray Q.sub.3, and the exit angle thereof will accordingly become small, thereby the effective illumination area will become small.

On the other hand, when the value of the focal length f.sub.2 is larger than 1.55f, the image of the entrance pupil which is placed at the conjugate position to the object will become small, since the magnification is in inverse proportion to the value f.sub.2 due to the conjugate relationship between the entrance pupil and the object. In this case, since the refracting power of the second lens will become small, it will accordingly be impossible that the exit angle of the rays entering at relatively large incident height cannot be controlled to be small independent of the size of the light source, thereby the irradiance on the object will be rapidly reduced particularly in the intermediate area through the peripheral area of the object.

Hereinafter described are examples of the optical system of this embodiment. In the following examples, the optical system L (i.e. optical system 3 in FIG. 9) is designed so that the diameter of the light source=17.64 (maximum incident angle: .omega..sub.max =10 degrees); the distance a between the light source and the entrance pupil A=50; the distance between the rear surface of the second lens and the object=100; the diameter of the object=90 (maximum exit angle .theta..sub.max =24.2 degrees); the effective diameter of the lens=1.0; and the synthesized focal length of the optical system as a whole=1.0. The optical system is further designed so that the entrance pupil A is placed at the front surface of the first lens L.sub.1, and that the image of the entrance pupil is imaged on the object.

Referring to FIG. 54, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 25.

FIG. 57 shows an irradiance distribution on the object, from which it will be understood that it is within the range of .+-.4 percent. This example is the case where the focal length f.sub.2 is approximately of maximum value.

Referring to FIG. 58, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 26.

FIG 59 shows an irradiance distribution on the object, from which it will be understood that the it is within the range of .+-.4 percent. This example is the case where the value of (d.sub.3 /r.sub.4) is of the minimum value.

Referring to FIG. 60, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 27.

FIG. 61 shows an irradiance distribution on the object, from which it is understood that the irradiance reduction in the intermediate area is within several percent, and that the peripheral irradiance is rather increased several percent. This example is the case where the value of (d.sub.3 /r.sub.4) is of maximum value.

Referring to FIG. 62, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 28.

FIG. 63 shows an irradiance distribution on the object, from which it is understood that the irradiance in the peripheral area is sufficiently increased. This example is the case where the focal length f.sub.2 is the shortest among the examples.

Referring to FIG. 64, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 29.

FIG. 65 shows an irradiance distribution on the object, from which it is understood that the irradiance in the peripheral area is sufficiently increased.

Referring to FIG. 66, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 30.

FIG. 67 shows an irradiance distribution on the object, from which it is understood that the irradiance reduction in the intermediate area is within several percent, whereas the irradiance in the peripheral area is slightly increased.

According to a further feature of the present invention, the optical system 3 employed in the illumination apparatus shown in FIG. 9 includes two optical units including two lenses, the first optical unit comprising a single positive lens and having a convex rear surface the second optical unit comprising a single positive lens and having a concave front surface and a convex rear surface, the optical system being designed to satisfy the following formulae:

where f is a synthesized focal length of the optical system as a whole; r.sub.2, r.sub.3, and r.sub.4 are a radius of curvature of the rear surface of the first optical unit, of the front and rear surfaces of the second optical unit, respectively; and n.sub.1 and n.sub.3 are refractive indexes of the first and second optical units.

In this embodiment, both the distance a between the light source and the front surface of the optical system and the distance b' between the rear surface of the optical system and the object are sufficiently large in comparison with the synthesized focal length f. The intermediate image of the light source is formed in the vicinity of the second lens, whereas the image of the entrance pupil A is formed on the object by the second lens.

This embodiment performs substantially the same functions as the fourth embodiment. For example, as shown in FIG. 69, the incident rays entering into the optical system are subject to the refracting power of the rear surface of the first lens L.sub.1, and the larger the incident height of the ray entering, the more strongly the refracting power of the rear surface of the first lens acts on the same due to the spherical aberration. The intersection I.sub.1 of both marginal rays Q.sub.1 and the optical axis Z accordingly is located before the intersection I.sub.2 of both the paraxial rays Q.sub.2 and the optical axis.

The rear surface r.sub.4 of the second lens L.sub.2 is located behind the intersections I.sub.1 and I.sub.2 and has a strong refracting power. The refracting power of the surface r.sub.4 will not act on the marginal ray Q.sub.1, and the diverging function will rather act on the paraxial ray Q.sub.2. The optical system of this embodiment controls the exit angle of the rays entering at relatively large incident height, so that the irradiance reduction in the peripheral area of the object is effectively resolved.

The rear surface of the first lens L.sub.1 affects the positive coma, which implies that the rear surface r.sub.2 of the first lens L.sub.1 is defined within the range where the incident height to the rear surface r.sub.4 of the second lens L.sub.2 of a marginal ray Q.sub.3 will not become excessively large, as can be seen in FIG. 70. This is because, when the incident height to the rear surface r.sub.4 of the second lens is excessively large, the exit angle .theta. therefrom will, to the contrary, become excessively small due to the refracting power of the surface r.sub.4, and the effective illumination area will accordingly become small.

The optical system of this embodiment is designed to satisfy the formulae (90) and (91):

The formula (91) requires that the irradiance distribution on the object be uniform or increased in the peripheral area thereof, and that a wide illumination area be ensured. Both the sum of the refracting powers of the rear surface of the first lens L.sub.1 and of the front surface of the second lens L.sub.2, and the refracting power of the second lens will affect the conjugate relationship between the entrance pupil and the object.

When the value of {(1-n.sub.1)/r.sub.2 +(n.sub.3-1)r.sub.3 }f is smaller than -0.68, an intermediate image at the entrance pupil will become excessively small, hence the effective illumination area will become small.

On the other hand, when the value of {(1-n.sub.)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f is larger than 0.90, the refracting power of the rear surface of the second lens will become small in order to keep the conjugate relationship. The rear surface r.sub.4 of the second lens will not significantly affect the irradiance distribution, and accordingly, when the value of {(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f is larger than 0.90 and the value of {(1-n.sub.3)/r.sub.4 }f is smaller than 0.67, the irradiance reduction in the intermediate area becomes excessively large, and further the irradiance in the peripheral area becomes decreased.

Hereinafter described are examples of the optical system of this embodiment. In the following examples, the optical system L (i.e. optical system 3 in FIG. 9) is designed so that the diameter of the light source=17.64 (maximum incident angle: .omega..sub.max =10 degrees); the distance a between the light source and the entrance pupil=50; the distance between the rear surface of the optical system and the object=100; the diameter of the object=90 (maximum exit angle .theta..sub.max =24.2 degrees); the effective diameter of the lens=1.0; and the synthesized focal length of the optical system as a whole=1.0.

Referring to FIG. 68, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 31.

FIG. 71 shows an irradiance distribution on the object, from which it is understood that irradiance reduction in the intermediate area is within 3 percent, and that the irradiance in the peripheral area is effectively increased. This example is a standard case among the examples.

Referring to FIG. 72, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 32.

FIG. 73 shows an irradiance distribution on the object, from which it is understood that irradiance reduction in the intermediate area is within several percent, and that the irradiance in the peripheral area is to the contrary increased several percent.

This example is a standard case where the value of {(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f is close to the maximum value of the conditional formula (90) and the value of {(1-n.sub.3)/r.sub.4 }f is close to the minimum value of the formula (91).

Referring to FIG. 74, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 33.

FIG. 75 shows an irradiance distribution on the object, from which it is understood that irradiance reduction in the intermediate area is within several percent, and that the irradiance in the peripheral area is sufficiently increased.

Referring to FIG. 76, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 34.

FIG. 77 shows an irradiance distribution on the object, from which it is understood that irradiance reduction in the intermediate area is within several percent, and that the irradiance in the peripheral area is sufficiently increased.

Referring to FIG. 78, which shows a side view of the optical system 3 of this example, the optical system comprises two optical units including two lenses L.sub.1 and L.sub.2, wherein the optical system satisfies the following formulae:

The lens data of this optical system are shown in Table 35.

FIG. 79 shows an irradiance distribution on the object, from which it is understood that the irradiance is within .+-.3 percent throughout the object.

In the aforementioned embodiments, the optical system 3 is formed into a so-called fly's eye configuration, in which a plurality of element lenses are aligned two-dimensionally. Such fly's eye configuration is especially advantageous for use in an illumination apparatus.

According to the preset invention, in the case where a projection lens 6 is disposed behind an object to be illuminated (i.e. an original 5), as shown in FIG. 9, the irradiance distribution on a photosensitive material 7 will be uniform throughout the entire surface thereof despite the cosine fourth law caused by the projection lens. The examples where the irradiance is gradually increased in the peripheral area of the object may particularly be adaptable for obtaining a uniform irradiance on the photosensitive material. For instance, when the example shown in FIGS. 10 and 11-(A) through 11-(C) is employed in the optical system 3 shown in FIG. 9, the irradiance distribution will be uniform on the photosensitive material 7, which irradiance distribution is shown in FIG. 80.

Referring to FIG. 81, which shows another illumination apparatus according to the present invention, the structure of the illumination apparatus is basically the same as that shown in FIG. 9 except an application of a Fresnel lens. The Fresnel lens 81 is designed that the focal length thereof is 1200 mm, and is disposed between the diffusing plate 4 and the original to be illuminated 5.

When the Fresnel lens 81 is placed in the manner described above, the irradiance in the peripheral area of the photosensitive material 7 will be reduced according to the cosine third law. The application of the optical system 3 will, however, correct the irradiance distribution on the photosensitive material 7, and the resultant irradiance distribution thereon is shown in FIG. 82, which is obtained by employing the example shown in FIG. 10 in the optical system 3 shown in FIG. 81. It will be understood that the irradiance distribution on the photosensitive material is well corrected and is within .+-.5 percent.

The aforementioned embodiments are in the case where no vignetting is caused. Some projection lenses may often cause the vignetting, as the field angle .theta..sub.1 thereof increases. In this case, the irradiance on the object to be illuminated can be expressed by the product of both cos .sup.4 .theta..sub.1 and the vignetting factor of the projection lens to be used.

FIG. 83 shows an example of the vignetting factor of a projection lens. In the case where the illumination apparatus shown in FIG. 81 is used, which case will cause the irradiance reduction according to the cosine third law, the irradiance distribution on the photosensitive material 7 results as shown in FIG. 84, from which the irradiance distribution is within .+-.5 percent.

While the invention has been illustrated and described as embodied in specific forms of illumination apparatus, it is not intended to be limited to the details shown, since various modifications and structural changes may be made without departing in any way from the spirit of the present invention.

Without further analysis, the foregoing will so fully reveal the gist of the present invention that others can, by applying current knowledge, readily adapt it for various applications without omitting features that, from the standpoint of prior art fairly constitute essential characteristics of the generic or specific aspects of this invention.

What is claimed as new and desired to be protected by letters patent is set forth in the appended claims.