Plastic Lens

1. Field of the Invention

The present invention relates to a plastic lens to be used for an optical system (laser optical system) for a laser light source, and more particularly to a plastic lens suitable for use in a lens of a laser scanning optical system of a laser beam printer or a pickup optical system for an optical disk.

2. Related Background Art

A lens made of a glass material has been used in the optical system of the optical pickup and the optical system of the laser beam printer.

When a lens to be used in the optical system for the laser light source (hereinafter referred to as a laser optical system) is made of polymethyl methacrylate resin and a temperature and a humidity which are environmental conditions of the optical system are changed (for example, 20.degree. C., 50% to 50.degree. C., 95%), an optical performance usually varies so that a focus point significantly varies.

The variation of the focus point greatly depends on a lens shape, particularly a ratio D/H of a lens thickness D and a lens outer diameter (or lens height) H.

When the lens for the laser optical system is made of polycarbonate resin or polystyrene resin, the variation of the focus point due to the change of humidity of the environmental condition is smaller.

However, when beam shapes before and after the laser beam passing through the lens are compared, the beam shape of the laser beam before it passes through the lens is generally circular while the beam shape of the laser beam after it passes through the lens is elliptic or divided into two parts like a figure "8".

On the other hand, when the laser beam passes through a lens made of polymethyl methacrylate resin, the variation of the focus point due to the change of humidity is large but the change of the beam shape before and after the light beam passes through the lens is not significantly changed.

It is an object of the present invention to provide a plastic lens which compensates for a variation of an optical performance of the plastic lens to a humidity, particularly a variation of a focus point of properly designing a shape of the lens and also effectively compensates for deterioration of a shape of a laser beam after the passage of the laser beam through the plastic lens.

The plastic lens of the present invention to be used for an optical system for a laser light source is made of a plastic material having a modulus of photoelasticity at 632.8 nm of larger than zero and no larger than 60.times.10.sup.-13 cm.sup.2 /dyne and has such a lens shape that W.times.D/H is larger than zero and no larger than 4, where D is a maximum thickness of the plastic lens along an optical axis in a light beam effective diameter, H is a lens outer diameter and W is a saturation moisture absorption factor (%) of the plastic material at the temperature of 50.degree. C. and the humidity of 95%.

FIG. 1 shows a sectional view of an embodiment-1 of the lens of the present invention,

FIG. 2 shows a sectional view of an embodiment-2 of the lens of the present invention,

FIG. 3 illustrates a refractive index distribution caused by the impregnation of moisture into the lens,

FIG. 4 illustrates a refractive index distribution in a section A-A' of FIG. 3,

FIG. 5 illustrates a change in the refractive index distribution due to the impregnation of the moisture into the lens,

FIG. 6 illustrates a change in a focus point due to the change in the refractive index distribution of the lens of FIG. 5;

FIG. 7 illustrates a refractive index distribution caused in the lens by the impregnation of the moisture into the lens,

FIG. 8 illustrates a change in a modulus of photoelasticity of a plastic material,

FIG. 9 illustrates a change in a modulus of photoelasticity of a plastic material,

FIG. 10 shows a schematic view of an embodiment in which the plastic lens of the present invention is applied to a laser beam printer,

FIG. 11 shows a sectional view of the plastic lens,

FIG. 12 shows a schematic view in which the plastic lens of the present invention is applied to an optical system of a pickup for an optical disk, and

FIG. 13 illustrates a shape of a section of a collimator lens 2 of FIG. 10.

FIGS. 1 and 2 show sectional views of lenses in embodiments 1 and 2 of the plastic lens PL of the present invention. The plastic lens PL of FIG. 1 is a positive lens and a plastic lens PL of FIG. 2 is a negative lens.

D denotes a maximum thickness of the plastic lens PL along an optical axis in a light beam effective diameter, and H denotes an outer diameter (lens height) of the plastic lens PL.

In the present embodiment, a modulus of photoelasticity C of the material of the plastic lens PL, a maximum thickness D, a lens outer diameter H and a saturation moisture absorption factor W are defined as described above to effectively compensate for the variation of the focus point (the variation of the refractive power) caused by the change in humidity of atmosphere and the deterioration of a shape of light beam after the passage through the lens.

Characteristics of the plastic lens of the present invention are now explained.

The focus point of the plastic lens used in the laser optical system significantly changes when the environmental humidity changes. Regarding this fact, it has been found that it correlates to a refractive index distribution of the material caused in the lens.

FIG. 3 shows a distribution of density caused in the plastic lens PL by the impregnation of moisture into the lens when the lens is placed from a room temperature and room humidity environment to a high humidity environment. The density distribution is substituted by a refractive index distribution by the Lorentz-Lorenz's formula and the refractive index is high in an area into which the moisture has impregnated. In this case, a refractive index distribution caused in a section (section A-A' in FIG. 3) normal to the travelling direction of the laser beam significantly affects to the variation of the focus point. (See FIG. 4 which shows the refractive index distribution in the section A-A' of the plastic lens PL of FIG. 3) The refractive index distribution changes from time to time as the moisture impregnates and the focus point also changes from time to time accordingly.

FIGS. 5 and 6 illustrate such the aspect. When the lens made of polymethyl methacrylate resin is used, the refractive index before the test is substantially uniformly 1.491. When it is moved from the room temperature and room humidity environment to the high humidity environment, the refractive index on an end face of the plastic lens first changes to 1.493, and the change of the refractive index thereafter gradually extends to the center of the lens and the refractive index approaches to 1.493 as shown in FIG. 5.

Assuming that the shape of the plastic lens PL is fixed, a maximum displacement X.sub.MAX (see FIG. 6) of the focus point is proportional to a maximum refractive index distribution (=maximum differential refractive index) N.sub.MAX (see FIG. 5) in the section A-A' of FIG. 3 and it is expressed by:

where B.sub.1 is a constant.

The maximum refractive index distribution (=maximum differential refractive index) N.sub.MAX is also proportional to the saturation moisture absorption factor W (%) of the plastic material and it is expressed by:

where B.sub.2 is a constant.

In the present embodiment, the saturation moisture absorption factor W (%) is given by

where Wo is a weight of the plastic lens in an absolute dry state, and Wa is a weight of the plastic lens when the plastic lens is left in an environment of a temperature of 50.degree. C. and a humidity of 95% until the change in the weight ceases. Assuming that the shape of the plastic lens is constant, the following is met.

where B.sub.3 is a constant.

The refractive index distribution in the plastic lens greatly varies with the lens shape. In the plastic lens having the lens shape shown in FIG. 3, the impregnation of the moisture through the lens plane 25 is dominant. On the other hand, in a plastic lens PL having a lens shape shown in FIG. 7, the impregnation through a peripheral surface 71 is dominant. The displacement of the focus point is larger in the plastic lens shown in FIG. 7 than in the plastic lens of FIG. 3.

Assuming that the saturation moisture absorption factor of the plastic material is constant, the maximum refractive index distribution N.sub.MAX in the section A--A' of the lens of FIG. 3 is proportional to the ratio D/H of the maximum thickness D of the plastic lens along the optical axis in the light beam effective diameter and the effective lens diameter (lens height) H as defined in FIGS. 1 and 2, and it is expressed by

where B.sub.4 is a constant.

Since the maximum refractive index distribution N.sub.MAX is proportional to the maximum focus point displacement X.sub.MAX as described above, the following is met.

where B.sub.5 is a constant.

Thus, the maximum focus point displacement X.sub.MAX is determined by the saturation moisture absorption factor W (%) of the plastic material and the ratio D/H of the maximum thickness D and the effective lens diameter H. From the formulas (1) and (2), the following condition should be met in order to meet a predetermined optical performance.

where B.sub.6 is a constant.

Namely, where a material having a large saturation moisture absorption factor W (%) is used, the ratio D/H should be small, and where a material having small W (%), the ratio D/H may be large.

It is preferable from the standpoint of the optical performance required for the laser optical system that the products W.times.D/H of the ratio D/H and the saturation moisture absorption factor W (%) of the plastic material at a temperature of 50.degree. C. and a humidity of 95% is larger than zero and no larger than 4, where D is the maximum thickness of the plastic lens in the light beam effective range and H is the effective lens diameter.

It has been found that the deterioration of the spot shape of the laser beam after it passes through the plastic lens is determined by a modulus of photoelasticity of the plastic material.

When the plastic lens is formed, a shearing stress or a thermal stress remains in the lens depending on a manner of flow and cooling of the plastic material. Those residual stresses cause double refraction in proportion to a modulus of photoelasticity of the plastic material.

The following relation is met

where .DELTA.n is an amount of double refraction, C is a modulus of photoelasticity and S is a residual stress.

The deterioration of the spot shape of the light beam is determined by the amount of double refraction (.DELTA.n) in the plastic lens. The amount of double refraction .DELTA.n is determined by two variables, the modulus of photoellasticity C of the plastic material and the residual stress S. In case of forming a plastic lens, a molding should be conducted so as not to occur a sinkmark. Since certain amount of residual stress S inevitably occurs, S may be regarded as a constant. Accordingly the double refraction occurs in proportion to the modulus of photoelasticity C which is inherent to the material.

In the present invention, the plastic lens material for the laser optical system has the modulus of photoelasticity C at a wavelength of 632.8 nm of larger than zero and no larger than 60.times.10.sup.-13 cm.sup.2 /dyne in order to attain a good optical performance. The saturation moisture absorption factors W at the temperature of 50.degree. C. and the humidity of 95% and the moduli of photoelasticity C at the wavelength of 632.8 nm, of representative plastic lenses are shown in Table 1.

In a copolymer of an acrylate compound and a stylene compound or a mixture of a polymer of its compound, the modulus of photoelasticity C significantly changes with a compounding ratio thereof as shown in FIG. 8.

When MS resin is used, a compounding ratio of methyl methacrylate and sthylene is set to

in order the modulus of photoelasticity C at the wavelength of 632.8 nm to meet the condition of larger than zero and no larger than 60.times.10.sup.-13 cm.sup.2 /dyne. The upper limit MMA/St=100/0 means that MMA is included at 100% and it means PMMA resin.

When the copolymer of the carbonate compound and the sthylene compound or mixture of polymer of its compound is used, the modulus of photoelasticity C significantly changes with weight ratios of the constituents as shown in FIG. 9. In the present invention, the following condition is met;

where Mpc is a weight of polycarbonate constituent and Mps is a weight of sthylene compound polymer constituent in order for the modulus of photoelasticity C at the wavelength of 632.8 nm to meet the condition of no larger than 60.times.10.sup.-13 cm.sup.2 /dyne.

FIG. 10 shows a schematic view of a first embodiment of the present invention which uses the plastic lens of the present invention. The present embodiment is applied to a laser scan optical system of a laser beam printer. Numeral 1 denotes a laser diode as a light source, numeral 2 denotes a collimator lens and numeral 3 denotes a cylindrical lens. A laser beam from the laser 1 is focused on a surface of a polygon mirror 4 by the collimator lens 2 and the cylindrical lens 3.

The light source 1 through the polygon mirror 4 form a primary focusing system. Numeral 5 denotes a spherical lens and numeral 6 denotes a toric lens. An f.theta. lens system is constructed by the spherical lens 5 and the toric lens 6. The laser beam transmitted through the spherical lens 5 and the toric lens 6 is reflected by a reflection mirror 7 and focused on a photosensitive drum 10. The polygon mirror 4 to the photosensitive drum 10 form a secondary focusing system.

In the present embodiment, the collimator lens 2, the cylindrical lens 3 the spherical lens 5 and the toric lens 6 in FIG. 10 are made of plastic materials. The moduli of photoelasticity C of the plastic lens materials at the wavelength of 632.8 nm to meet the optical performance as the laser beam printer are shown in Table 2.

In Table 2, the copolymers (MS resin) of methyl methacrylate and sthylene of various compounding ratios which meet the modulus of photoelasticity between 7 and 90 are shown. Some compositions exhibit somewhat white turbidity depending on the compounding ratio of the methyl methacrylate and sthylene but it is of a level which does not affect to the measurement.

Table 2 indicates that when the collimator lens is substituted by a plastic lens made of a plastic material and other lenses, that is, the cylindrical lens, the spherical lens and the toric lens are glass lenses, for example, the modulus of photoelasticity of the plastic material of the collimator lens at the wavelength of 632.8 nm should be no larger than 10.times.10.sup.-13 cm.sup.2 /dyne.

As seen from Table 2, the farther the lens is optically displaced from the laser diode 1, the less severe is the required characteristic of the plastic lens, but the modulus of photoelasticity of even the toric lens 6 at the wavelength of 632.8 nm should be larger than zero and no larger than 60.times.10.sup.-13 cm.sup.2 /dyne in order to keep the required optical performance.

The displacement of the focal point as the change in the optical performance which is caused when the plastic lens is moved from a room temperature and room humidity environment to a high humidity environment (for example, temperature of 50.degree. C. and humidity of 95%) in a conventional laser beam printer is discussed below.

FIG. 11 shows a shape of a section taken along a center line of the toric lens 6. The light beam effective range S is 3 mm and the maximum thickness D within that range is 20 mm. The effective lens diameters (lens heights) H required for the toric lens 6 when it is made plastic materials having different saturation moisture absorption factors at the temperature of 50.degree. C. and the humidity of 95% are shown in Table 3.

As for the material having the saturation moisture absorption factor of smaller than 0.8%, the effective lens diameter H is within the light beam effective range. Therefore, the effective lens diameter H was not measured for such toric lens 6.

As seen from Table 3, the product W.times.D/H of the ratio D/H and the saturation moisture absorption factor W (%) of the plastic material at the temperature of 50.degree. C. and the humidity of 95%, where D is the maximum thickness in the light beam effective range and H is the effective lens diameter, meets the condition of greater than zero and no greater than 4 to maintain a good optical performance.

It is preferable that the values of W.times.D/H of the collimator lens, the cylindrical lens and the spherical lens are smaller than that of the toric lens.

This is explained below for the collimator lens 2.

Since the collimator lens 2 is disposed closest to the laser diode 1, the required precision for the change of humidity is severe as it is for the modulus of photoelasticity.

A shape of a section of the collimator lens 2 of FIG. 10 is shown in FIG. 13. The light beam effective range S is 1.5 mm and the maximum thickness D within that range is 8 mm.

The effective lens diameters (heights) H required for the collimator lens 2 when it is made by plastic materials having different saturation moisture absorption factors at the temperature of 50.degree. C. and the humidity of 95% are shown in Table 4.

As seen from Table 4, a good optical performance of the collimator lens is maintained when the ratio D/H of the maximum thickness in the light beam effective range and the effective lens diameter H is larger than zero and no larger than 4 and the products W.times.D/H of the ratio D/H and the saturation moisture absorption factor W (%) of the plastic material at the temperature of 50.degree. C. and the humidity of 95% is larger than zero and no larger than 0.2.

FIG. 12 shows a schematic view of a second embodiment which uses the plastic lens of the present invention. The present embodiment is applied to an optical system of a pickup for an optical disk. Numeral 12 denotes a laser diode as a light source, numeral 13 denotes a collimator lens for collimating the laser beam, numeral 14 denotes a grating, numeral 15 denotes a beam splitter, numeral 16 denotes a detector lens, numeral 18 denotes a photo-detector, numeral 19 denotes a wavelength plate, numeral 20 denotes an objective lens and numeral 22 denotes pits formed on a disk 23.

In the present embodiment, the laser beam emitted from the laser diode 12 passes through the collimator lens 13 and the grating 14 and is directed to the beam splitter 15. It is reflected thereby at a right angle, passes through the wavelength plate 19 and the objective lens 20 and is directed to the disk 23 on which the pits 22 are formed. The laser beam reflected by the disk 23 goes back along the initial path through the objective lens 20 and the wavelength plate 19, is reflected by the reflection plane of the beam splitter 15 at a right angle, passes through the detector lens 16 and is directed to the photo-detector 18.

In the embodiment of FIG. 12, the collimator lens 13, the objective lens 20 and the detector lens 16 are made by plastic materials.

The moduli of photoelasticity C of the lens materials at the wavelength of 632.8 nm required to meet the optical performance as the optical system of the optical disk are shown in Table 5. The measurement is same as that of the embodiment 1 described above.

In the optical system of the pickup for the optical disk, the requirement for the objective lens is least severe as shown in Table 5. Even for the objective lens, however, it is preferable that the modulus of photoelasticity at the wavelength of 632.8 nm is larger than zero and no larger than 60.times.10.sup.-13 cm.sup.2 /dyne in order to maintain a good optical performance.

The variation of the focus point as the change of optical performance caused when the environmental humidity changes is discussed below.

The plastic lens of FIG. 1 shows the shape of the objective lens 20 under such the condition.

The light beam effective range is 1.5 mm and the maximum thickness D within that range is 6 mm.

The effective lens diameters (lens heights) H required for the plastic lens 20 when it is made by plastic materials of different saturation moisture absorption factors at the temperature of 50.degree. C. and the humidity of 95% are shown in Table 6.

As for the material having the saturation moisture absorption factor of smaller than 1.2%, the effective lens diameter is within the light beam effective range. Therefore, the effective lens diameter is not measured.

In the present embodiment, the product W.times.D/H of the ratio D/H and the saturation moisture absorption factor W (%) of the plastic material at the temperature of 50.degree. C. and the humidity of 95%, where D is the maximum thickness in the light beam effective range and H is the effective lens diameter is larger than zero and no larger than 4 as shown in Table 6 in order to maintain a good optical performance.

It is preferable that the products W.times.D/H of the collimator lens and the detector lens are smaller than that of the objective lens.

In accordance with the present invention, when the plastic lens is used for the optical system of the laser light source, the plastic material having the modulus of photoelasticity at the wavelength of 632.8 nm of greater than zero and no greater than 60.times.10 .sup.-13 cm.sup.2 /dyne is used and the product W.times.D/H of the ratio D/H of the maximum thickness D of the lens along the optical axis in the light beam effective range and the effective lens diameter H, and the saturation moisture absorption factor W (%) of the plastic material at the temperature of 50.degree. C. and the humidity of 95% is selected to be larger than zero and no larger than 4. As a result, the plastic lens which solves the problems of the deterioration of the beam shape due to the double refraction and the change of the focus point as the change of the optical performance caused by the change of the environmental humidity is attained.