Athermalized Diffractive Optical Elements

The present invention relates to diffractive optical elements ("DOEs") and particularly diffractive lenses. The invention provides a diffractive lens which is athermalized so that it maintains its effective or back focal length to an image plane ("EFL") over a temperature range extending above and below room temperature, and a method of making such an athermalized diffractive lens.

The invention is especially suitable for use in providing diffractive field lenses which image an object over a wide enough field of view to be useful in photographic cameras, and has the advantage of providing such a lens which is corrected for spherical and chromatic aberration as well as aberration due to thermal expansion and contraction.

Various types of hybrid diffractive/refractive lenses and a proposal for athermalizing such lenses appears in U.S. Pat. No. 5,260,828 issued to Londono, et al., on Nov. 9, 1993. Athermalization, as proposed in the patent, is based upon the power (the reciprocal of the focal length) of the refractive part of the hybrid lens changing in an opposite sense to the power of the diffractive part of the lens, with changes in temperature. The Londono, et al. patent provides power compensation by designing both parts of the lens with sufficient power so that the sum of the powers provides the desired power notwithstanding thermal expansion and contraction of the body of the lens. The zone spacings are optimized for room temperature and are not changed to compensate for changes in power due to thermal expansion and contraction.

In accordance with the invention, athermalizing is obtained to the annular grating lines by making slight differences in the zone widths (the radial distance in the case of a diffractive lens) so that they differ from the zone widths for the optimum room temperature design. Compensation occurs because, over a temperature range, expansion and contraction in the zone dimensions compensates for thermal expansion/contraction effects over the range. At the same time, the zone spacings provide for minimizing spherical and chromatic aberration as well as for maintaining focus (EFL and power). In a DOE lens having a plurality of zones which are adjacent to each other and are spaced successively in a radial direction from the optimum axis of the lens, alternate zone spacings are increased and decreased from zone spacing for the optimum room temperature design. The spacings are also selected so as to achromatize the lens and correct for spherical aberration and may also be corrected for coma astigmatism distortion and field curvature ("Petzval") aberration.

Accordingly, it is an object of the present invention to provide an improved DOE.

It is a still further object of the present invention to provide an improved DOE which is athermalized over a temperature range, and to an improved DOE lens which maintains focus over this range notwithstanding increases or decreases in dimensions with thermal expansion and contraction.

It is a still further object of the present invention to provide an improved diffractive/refractive hybrid lens which is suitable for use as a field lens in photographic camera applications.

It is a still further object of the present invention to provide an improved diffractive lens in which spherical and chromatic aberration is corrected along with maintenance of focus over a desired temperature range, which may be at least 15.degree. C. above and below room temperature in optical material such as glass and plastics, and even germanium for infrared applications.

It is a still further object of the present invention to provide an improved DOE lens having fewer zones than lenses such as shown in the above reference Londono patent.

Briefly described, the invention provides an improved diffractive optical element and method of manufacturing same and utilizes a body of optically transmissive material subject to changes in dimensions with temperature. The body has at least on one surface thereof, a plurality of lines which define a DOE. In the case of a DOE lens, these lines may be annular lines about an optical axis of the lens and may be the steps of a blaze having ramps which define the radial zone spacing of the lens. The zone spacing or width between the lines is varied as a function of temperature in an amount sufficient to athermalize the DOE across a range of temperature.

The foregoing and other objects, features and advantages of the invention as well as presently preferred embodiments thereof will become more apparent from a reading of the following description in connection with the accompanying drawings:

FIG. 1 is a diagrammatic cross-section of a hybrid refractive/diffractive singlet embodying the invention;

FIG. 2 is a diagrammatic view illustrating the first three zones of the DOE of the lens shown in FIG. 1 showing the spacing of alternate zones being increased and decreased from the spacing at a mean temperature, which may be room temperature, and which illustrates the principle of the invention.

FIGS. 3A to AJ are a series of plots illustrating the performance of a hybrid diffractive/refractive lens (DOE) and particularly the performance of the meniscus lens, the design of which is set forth in chart C presented below. FIGS. 3A to I show the design's performance without athermalization in accordance with the invention at room temperature to form comparison with the performance of the athermalized lens at room temperature (FIGS. 3J to R), at -15.degree. C. (FIGS.>S to AA), and at +15.degree. C. (FIGS. AB to AJ).

Normal diffractive zone spacing, r, is defined by a phase polynomial .phi.(r), given by the equation

where S.sub.1 . . . S.sub.n+1 are aspheric coefficients of the emerging wavefront, m is the order number, and .lambda. is the design (central) wavelength. Physical construction consist of blazed zones, which are ramps with circular-shaped heights of steps. These interact with incident light to function as phase transformations, since each zone gives an optical phase difference of 2.pi..

Refractive/diffractive hybrid lenses are optimized to focus at room temperature. Zonal radii enclose equal areas (Fresnel Zone Plates) and therefore expand or contract in accordance to whether the lens is heated or cooled. The effect of temperature change is for the lens to lose some of its required focal ability. To compensate for temperature, according to this invention, a change is made in construction by modifying the normal zonal spacings. That is, zone spacings for an athermalized lens takes into account dimensional changes through use of discrete adjustments in the S-coefficients. With this technique, one-half of the alternating zones are in their correct focal position for either the expanded or contracted temperature variations when the bulk lens changes dimension. This is done by recalculating the S-coefficients, Eq. 1, to compensate for thermal shifts over an expected temperature range.

When a lens expands or contracts, its volume, refractive index, and surface curvatures change. Lens thickness and diameter expands or contracts. Spherical surfaces remain spherical, and aspheric surfaces become more or less aspherical. Focal lengths increase/decrease with respect to temperature changes that decrease/increase, respectively.

FIG. 1 shows a DOE lens on a plano surface (S2) of a body (L1) of optically transmissive material, such as any of the materials mentioned in the Londono patent referenced above. There are several zones around the optical axis (OA). An aperature Ap restricts the field on the image side of the lens. The body L1 between vertices had a thickness d.sub.1 (TH1). The aperature to rear vertex spacing is d.sub.2 (TH2). The EFL to the center of the curved image (Camera focal) plane is d.sub.1 +d.sub.2 =TH3. For clarity, the zonal radii along the diffractive surface are much enlarged. Of course, at the scale of the drawings, zone heights and spacings would not be visible. The on-axis zone always has the largest step interval; while widths between successive zones become closer together as their radii increase outward to full aperture. The paraxial approximation to the size of zonal radii r.sub.m and blaze height h.sub.max are given by the equations

where fo is the paraxial focal length or EFL, and .lambda.o is the central or design wavelength. Zone radii progressively enlarge according to Eq. 2, while areas encompassed between annular zones are equal. For an athermalized lens this relationship is no longer used, and alternating zones will have a slightly staggered pattern in radial distances from the optical axis.

To athermalize the DOE lens, zone spacings are first calculated by minimizing aberrations at room temperature. Over the temperature range of interest, two sets of S-coefficients are calculated, employing optimizations by additional optical design. To athermalize the lens, that is, to compensate for both thermal conditions, a single phase polynomial is now recalculated from these sets of two additional phase polynomials. Resulting, is a zone spacing which compensates for either temperature condition. This consolidation process can be considered as averaging two aberration properties, giving the best correction through compensation as the temperature changes on either side of room (or design) temperature. Resulting, is zonal spacings that produce a composite design giving satisfactory focal performance over an expected temperature range.

The methodology is explained in connection with FIG. 2; which again shows a few zones centered around the optical axis. Two temperature cases are considered: 1) zone radii expand at temperature T.sup.1, and 2) contraction to temperature T"; each with regard to a mean temperature T.sub.o. On either side of T.sub.o, there is a small radial shift, .DELTA..sub.ps corresponding to .DELTA..sub.p1 (hot) and .DELTA..sub.p2 (cold).

Shifts in radii are calculated from the .DELTA..sub.p differentials and radial compensations are made. Alternate zones are chosen as either the expanded or contracted radii in order to construct an augmented set for recalculating the new phase polynomial. For instance: zone #1 (hot) will be fabricated slightly short of its most expanded position by an amount r.sub.1 (T.sub.o)-(.DELTA..sub.p1), and the same for all odd-numbered radial zones, #3-(.DELTA.p.sub.3), --#5-(.DELTA..sub.p5), etc. This will compensate for a temperature raise. Compensation for a lower temperature will increase radii of even-numbered zones a slight amount r.sub.2 (T.sub.o)+.DELTA..sub.p2, for radial zone #2, and for successive even-numbered zones #4+(.DELTA..sub.p4), #6 (.DELTA..sub.p6), and etc. The array of alternate zones, even and odd, are tabulated in Chart A below; where sums +.DELTA..sub.p (even) and differences -.DELTA..sub.p (odd) are chosen in sequence. From this set, a computer program was devised that takes .DELTA..sub.p differences and corrects room temperature radii by calculating a new set of S-coefficients. The new set compensates for expansions ore contractions.

In constructing the hybrid lens (L1, FIG. 1), zonal radii may be diamond turned allowing for the requisite .DELTA..sub.p offsets. This fabrication is summarized in the charts, A and B, which show alternations required between the original zone spacings r.sub.1 (T.sub.o), r.sub.2 (T.sub.o) . . . r.sub.n (T.sub.o), and with a new set of radii increasing or decreasing with increments .DELTA..sub.p1, . . . .DELTA..sub.pn.

Only a few zones are shown in FIG. 2, but satisfactory performance and athermalization may be provided in a lens with about 10-20 zones.

Consider how the phase coefficients S.sub.n (Eq. 1) can be found, from which the zone widths are determinable using conventional techniques. The change in zone radius r.sub.m can, to first order, be expressed as

whereas .alpha..sub.g and .DELTA.T are the thermal coefficient of expansion of the material and the temperature differential, respectively. The refractive index will change by

Inserting Eq. 3 into the phase polynomial, Eq. 1, the size of zone radii can be calculated from ##EQU1## where b=.alpha..sub.g .DELTA.T. The set of five equations (Equations (5)) are binomial expansions in increasing powers of r.sup.n, where higher ordered terms are neglected. Equation (6) is the general equation for the binomial expansion for the S coefficients of the phase equation (1). Changes in zone heights, ›Eq. 2! will be negligible.

The set of five temperature altered phase coefficients, Eq. 5, are used to redefine a new athermal phase polynomial, described in the previous topics.

The athermal designed singlet lens provides a hybrid DOE with focal compensation over a prescribed temperature range. Focal aberrations at the film plane which are not acceptable for photographic camera applications can be accommodated by selecting curvatures and S-coefficients.

Chart C presented below indicates the curvatures and coefficients of the diffractive blazed surface on a meniscus lens which is athermalized in accordance with the invention. In chart C, the first column indicates the surface number, the second column indicates the curvature of the surface and the curvature of the base curve in the case of the DOE. The next column lists the phase coefficients of the DOE from which the zone radii and widths may be obtained in accordance with well known diffractive lens design techniques. The last column specifies the material in terms of index and Abbe number at room temperature and at the design wavelength of the lens which is 546 nm.

The asphere for Z(r) of Surface #1 is defined as follows ##EQU2## EP=Exponent 10.sup.P Surface # 2, number of zones=37

FIGS. 3A-C are MTF performance plots (three) taken at room temperature, To, for an incident wavelength of 546 nm for the lens design without the adjacent zone spacing for athermalizing the lens, which is the case also for the plots of FIGS. D-I. Fractional object heights are: (1) FOB 0 (0.degree. to the optical axis)--See FIG. 3A; (2) FOB 0.7 (22.degree. to the lens axis)--See FIG. 3B; and (3) FOB 0.9 (31-degree field angle)--See FIG. 3C. The curves in each plot are marked with a vertical dash, a square and a triangle for idealized tangential and sagittal measurements, respectively. The exemplary meniscus-type DOE (diffractive optical element) is designed to have an MTF of about 50% modulation at 60-cycles on-axis (scale is in cycles/mm). All field angles, FOB's, shows that the lens performs well as optimized at room temperature To. The top curve (marked with triangles) in all three plots (FIGS. 3A-C) shows the theoretical limit for a diffraction-limited, perfectly designed lens.

FIG. 3D shows point spread function (PSF) plots, which show the energy distribution, on-axis at the central focal spot. The focused beam is well within the design criteria of 30 microns at 50% of maximum intensity (scale in mm).

FIGS. 3E and F are opd fans which show difference in ray paths at the focal plane as a function of light rays transmitted across the lens diameter. There is a small departure from the desired, perfect spherical wavefront, showing astigmatism and coma aberrations, but minimized for a single-element lens (scale in wavelengths).

FIG. 3G is a plot of distortion at the film plane. Acceptable distortion should be no greater than 4% magnification--and is below 1%, in this lens exemplary DOE design (scale in percent).

FIG. 3H shows field sags, namely sagittal and tangential astigmatism that cannot be fully corrected in a simple lens, but is somewhat improved by the exemplary DOE and by using a curved film plane (in the long dimension, scale in wavelengths).

FIG. 3I plots lateral color. This plot shows that correction for chromatic aberration is provided across a spectrum of 440 nm to 650 nm. The lens design optimization includes minimum color separation in the film plane for primary color (blue to red) and secondary (blue to green) wavelengths, scale in mm.

FIGS. 3J-R are plots similar to FIG. 3A-I for the non-athermalized lens at room temperature. There is some degradation of the performance shown in FIGS. 3A-I, in a non-acceptable amount, including point spread function (PSF), 3M.

FIGS. 3S-AA are plots similar to FIGS. 3A-I, respectively, taken when the lens is cold (-15.degree. C.).

FIGS. 3AB-AJ are plots similar to FIGS. 3A-I, respectively, taken when the lens is hot (+15.degree. C.).

More specifically, the performance of the athermalized lens at low temperature (e.g., minus 15.degree. below temperature), at room temperature, and at high temperature (e.g., 15.degree. above room temperature) are indicated in the plots of modulation transfer function (MTF) at positions in the field both in the sagittal (x) and tangential (y) directions; as well as other aberrations. For instance, point spread function (PSF) shows a retained focal-spot size near or less than 20 microns root-mean-square diameter (at 50% peak height) over the athermalized range. Other important imaging aberrations are retained within acceptable levels for a single-element lens imaging onto a focal plane, like a film plane. In particular, unequal magnification due to distortion over the image plane is reduced and kept near constant at below 1%. Also of great importance, the kinoform-type lens remains corrected for lateral color, as reflected in plots of primary and secondary aberration taken over a wavelength range extending from 440 nm to 650 nm. Back focal length of the lens is maintained over a range compensating for thermal effects, as reflected in plots of optical path difference (OPD); while astigmatism, field sags, stays within imaging tolerance for a single element lens possessing no other lens elements. The temperature-induced optical response so sited thus illustrates the successful operation of an lens athermalized in accordance with the invention, as an imaging lens.

From the foregoing description, it will be apparent there has been provided an improved DOE and especially a DOE lens which is athermalized over a temperature range. Various embodiments of the invention have been described as well as the best mode of presently known for making such DOEs, thereby practicing in the invention. Variations and modifications in the herein described DOE lenses and methods of manufacturing same, within the scope of the invention, will undoubtedly suggest themselves to those skilled in the art. Accordingly, the foregoing description should be taken as illustrative and not in a limiting sense.