WO1999063367A1

WO1999063367A1 - Dispersing optical prism elements with graded index of refraction

Info

Publication number: WO1999063367A1
Application number: PCT/US1999/009295
Authority: WO
Inventors: Richard Blankenbecler; Andrew T. Zander; Ring-Ling Chien
Original assignee: Varian, Inc.
Priority date: 1998-06-04
Filing date: 1999-04-28
Publication date: 1999-12-09
Also published as: AU3871799A

Abstract

A focusing optical prism element for use in certain optical systems is provided. The prism has a front curved surface and a rear planar surface and contains a spatially varying index of refraction. It is termed a GRIN prism element. Compound prisms can be fabricated by combining a homogeneous lens with a GRIN prism. The gradient in the index of refraction can have an axial, cylindrical or more general profile geometry. If the gradient index is chosen so that the rear surface acts as a diverging lens, the chromatic dependence of the longitudinal focal length can be made small. A use of the GRIN prism as a dispersive element in a spectrograph is also described.

Description

DISPERSING OPTICAL PRISM ELEMENTS

WITH GRADED INDEX OF REFRACTION

FIELD OF THE INVENTION The present invention relates generally to unified focusing and dispersing prisms for use in optical systems, such as in beam transport, spectrographs and monochromators, and more particularly to lens-prism elements with a spatially varying, i.e. gradient, index of refraction.

BACKGROUND OF THE INVENTION

A conventional prism element with planar surfaces and with a homogeneous index of refraction can be used to guide light in a beam transport system. They can also be used to disperse, or to separate, light beams into their different wave length components. Dispersion occurs because the angle of refraction of the beam depends upon the index of refraction of the prism material. Since the index of refraction varies as a function of the wave length of the light, the outgoing light beam is color separated. In a spectrograph, the angular deflection of an outgoing light ray is related to its wave length. Thus a spectrograph allows one to study a wide band of the light spectrum simultaneously. A monochromator, on the other hand, isolates a very narrow band of wave lengths for study. Monochromators are used in several instruments; examples are instruments (termed spectrophotometers) used to measure transmittance and reflection as a function of wave length.

Spectrographs and monochromators are used to study light across a broad range of wave lengths. The three main classification regimes are termed the long wave lengths, infrared (IR), the visible region, and the ultraviolet (UV) which leads into the X-ray region of short wave lengths. The useful range in wave lengths for a prism instrument is limited by the transparency of the prism material. There are many possible choices for prism material that together allow a wide spectrum range to be spanned via overlapping regions. However, as stressed by Kingslake, "Disadvantages of prisms are their nonlinear dispersion and the very limited wave length range for which they are transparent." This quotation is found on page 1 in the general reference 'Applied Optics and Optical Engineering', edited by Rudolf Kingslake, Volume V, Optical Instruments Part II, Academic Press, New York 1969. It would therefore be useful to give the optical designer enhanced control over the nonlinear dispersion while using familiar and standard glass compositions that do not aggravate the transparency limitations.

Optical quality glass blanks that have a spatially varying index of refraction are commercially available from a variety of sources. These are termed gradient index blanks, or GRIN blanks, in the literature. The index profile can be axial, i.e., varying in only one spatial direction, cylindrical, or possess a more general spatial variation, as desired by the optical designer. GRIN blanks can be fabricated in a variety of materials that are suitable to cover the full wave length range. One of the useful properties of an index gradient is that it can affect the direction of a ray path of light while it passes through the gradient region. The general rule is that the ray will turn in the direction of the increasing index of refraction since that is the side of the ray that has the lowest propagation velocity. GRIN lens blanks are used to produce focusing lenses of the standard type with curved external surfaces generated by grinding and polishing.

For the infrared wave length range, gradient optical blanks can be made by several processes. In order to have suitable transmission properties in the IR the composition of the blank must be appropriately chosen. One of the most common choices for the IR region is zinc selenide or zinc sulfide for the active element. Suitable axial gradient index elements are commercially available from CVD, Inc. of Boston, MA; these blanks can be fabricated with a change in index as large as 0.2. In the visible range, the blanks for the fabrication of suitable optical gradient elements can be made by a variety of processes such as SOL-GEL, ion infusion, and atomic diffusion. In particular, there is the controlled diffusion processes that can produce macro lenses with a prescribable index of refraction axial profile. The fabrication of such axial gradient lenses by the controlled diffusion process is disclosed in U.S. Patent No. 5,262,896, "Refractive Elements With Graded Properties and Methods for Making Same," to R. Blankenbecler, which patent is incorporated herein by reference. These lenses are available from LightPath Technologies of Albuquerque, NM.

In the ultraviolet wave length range, optical blanks for the fabrication of gradient elements can be made by a few processes. In order to have suitable transmission properties in the ultraviolet, the composition of the element must be appropriately chosen. One of the best choices for the UV region is quartz or fused silica. Such gradient index elements can be made by the chemical vapor deposition (CVD) process. Selected geometries are available from several sources including the Heraeus Corporation of Duluth, GA.

All optical systems and instruments use optical elements to control the transfer properties of light. Of particular interest here are spectrographs and monochromators. There are many geometric layouts that have proven useful in these two instruments. A basic review of the prior art can be found in Chapter 3 entitled "Spectrographs and Monochromators" by R. J. Meltzer in the reference "Applied Optics and Optical Engineering", edited by Rudolf Kingslake, that was listed earlier. Another reference can be found in "The Principles of Optics" by A. C. Hardy and F. H. Perrin, McGraw-Hill, New York 1932 (starting on page 544). Instruments of these types have only utilized homogeneous optical dispersive prisms.

The dispersive power of the prism arises from the dependence of the index of refraction of the prism medium on the wave length of the incident light. An overall summary for homogeneous glass can be found in the book "Handbook of Glass Properties" by N. P. Bansal and R. H. Doremus, Academic Press, New York 1986. A general discussion can also be found in "Applied Optics" by L. Levi, John Wiley, New York 1982. The dispersion dependence of selected GRIN glass compositions has also been studied. For lead silicate glasses, useful for the near-infrared and visible regimes, a detailed study has been published by P. K. Manhart and R. J. Pagano entitled "Buchdahl Dispersion Model for Gradient Index Glass Families", SPIE Vol., Pages 2263-09 (1994). It is known that the index of refraction tends to increase ever more rapidly as the wave length decreases; this is the nonlinearity referred to above by Kingslake. Since all instruments require a detector in order to measure the position of the outgoing light energy, this nonlinearity severely complicates the design and construction of such detectors, as well as the interpretation of their output.

The use of a prism element to separate the different wave lengths of light also implies the use of conventional focusing optical elements to provide an image on a detector plane. This system usually requires several elements and requires very careful chromatic design so that the different wave lengths are focused sharply with no loss in resolution. GRIN prism elements allow a design with fewer elements, good chromatic properties, and improved performance. The use of axial index gradients for focusing in optical elements with tilted planar surfaces was described in US patents 5,541,774 and 5,703,722, both issued to Blankenbecler. These patents describe compound optical elements containing at least one internal tilted surface that exposes an axial index gradient whose profile is chosen to achieve focussing of light rays.

Thus, in certain designs the necessity for external spherical or cylindrical surfaces can be eliminated.

The use of an axial gradient optical element in a dispersing prism system such as a spectrograph was described in US provisional application 60/ 016,028 and in subsequent US serial no. 08/837,848. This invention exploits the fact that the angle of refraction at a surface and the angle of deviation caused by an index gradient in the interior of the optical element have different dependencies upon the wavelength of the light. Thus it is possible to use geometric designs that combine these two effects in different ways to achieve control over the dispersive power of the prism. Consequently, the wave length dependence of the dispersive power can be designed to optimize the performance and reduce the cost of the system. In contrast, older prior art systems would require several additional focusing and optical transport elements.

It is therefore an object of the invention to provide a prism design with dispersive and gradient index properties that, acting together, allow the simplified design and fabrication of spectrographs.

It is another object of the invention to provide a general framework that allows the designer to utilize GRIN prisms in a variety of useful forms and geometries.

It is a further object of the invention to provide a general framework that allows the designer to utilize appropriate GRIN prisms in a variety of wave length regimes, such as the infrared (long wave lengths), visible, and ultraviolet (short wavelength or X-rays).

SUMMARY OF THE INVENTION

The present invention utilizes prisms made out of glass blanks that have a spatially varying index of refraction. A gradient prism provides an optical element for the spectrograph designer that can be used to achieve many desirable optical functions. The basic property used in such instruments is that the index of refraction and its spatial derivative have a different dependence on wave length. The designer may choose to decrease the nonlinear dispersive behavior, in order to simplify the light detector, to improve the resolution of the instrument by increasing the nonlinear dispersion, or alternatively to make the dispersion very small for use in certain light beam guides. Therefore GRIN prisms can be used in various arrangements that combine these two properties in different ways to affect its overall dispersive properties. In one embodiment of the invention, an axial gradient wedge prism is provided having a spherical or cylindrical front surface, an optical axis, and a planar but tilted rear surface. The light rays refract as they pass through the curved front surface and refract again as they pass through the tilted rear surface. In addition the rays are very slightly bent by the axial gradient index as they traverse the interior of the prism. The total deflection of the rays is a combination of these mechanisms. Since these physical mechanisms have a different wave length dependence, it is possible to affect the overall dispersive power of the prism. The front surface is chosen to focus the rays with a chosen focal length. The refraction at the final tilted surface depends upon the index of refraction at the exit point and the wave length. If the index varies appropriately from the bottom to the top of the rear surface, the rays can be focused as from a positive or a negative cylindrical lens.

In another embodiment of the invention, the optical element consists of a compound lens/prism. The front section consists of a homogeneous lens with a spherical or cylindrical front surface. Its rear surface is preferably planar. The second element is a wedge prism with planar surfaces and possessing an index gradient. The front surface of the prism is arranged perpendicular to the optical axis of the lens. The light rays are refracted and focused as they pass through the front surface of the first element. To achieve the performance desired by the optical designer, the axial index of refraction of the prism element may be chosen to vary either along the optical axis or perpendicular to this axis.

In the above embodiments, the GRIN index profile of the prism can be either axial or cylindrical in geometry, or indeed, of more general variation.

BRIEF DESCRIPTION OF THE DRAWINGS The various features and advantages of the present invention may be more readily understood with reference to the following description taken in conjunction with the accompanying drawings.

Figure 1 A is a homogeneous wedge prism of the prior art. A sample ray is drawn. Figure IB is a two element compound homogeneous prism of the prior art. Figure 2A is a wedge prism with an index that varies along the optical axis.

Figure 2B is a wedge prism with an index that varies perpendicular to the optical axis. Figure 3 is a wedge GRIN prism with a curved front surface. Figure 4A is a compound element - a homogeneous lens and an axial GRIN wedge prism.

Figure 4B is a compound element - a homogeneous lens and a transverse GRIN wedge prism.

Figures 5A and 5B define the coordinates and quantities used in the theoretical treatment.

Figure 6 defines the coordinates and quantities used in further theoretical treatment. Figure 7A is a raytrace output from a commercial optical design package for a GRIN prism with spherical front surface.

Figure 7B is a raytrace output from a commercial optical design package for a GRIN prism with cylindrical diverging lens

DETAILED DESCRIPTION OF THE INVENTION

In accordance with the invention, a prism with a gradient index of refraction is provided. The angle of refraction of a light ray passing through a surface depends upon the angle between the ray and the normal to the surface and the indices of refraction on either side of the surface. The deflection of a light ray in passing through a gradient index medium depends upon the index gradient and the length of path in the GRIN region. The index of refraction has a different dependence on wave length than its spatial gradient. Thus the overall dispersion of the prism can be affected by combining these two mechanisms in different ways and ratios. The ratio of the two depends upon the vertex angle of the prism, the thickness (or path length) in the GRIN medium and the sign of the index gradient. The basic principles of homogeneous prisms of the prior art are illustrated in Figures

1 A, and IB and will be referenced below. The simplest GRIN prism is a wedge prism as shown in Figure 2 A and 2B. The dotted lines in all figures represent planes of constant value of the refractive index. Refraction takes place at the front and rear surfaces. The deflection due to the index gradient takes place as the ray passes through the wedge GRIN medium. The dispersive behavior of the total deflection angle depends upon the mixture of these effects. In Figure 2A and 2B, a ray at normal incidence parallel to the prism axis is not deflected as it enters the prism. As the ray traverses the medium, it is bent by the transverse refraction index gradient in Figure 2B. The ray is again refracted as it leaves the prism. The prescribability of the resultant dispersive power of the prism is achieved by the combination of these various effects. The dispersive effects of the index of refraction is different from the dispersive effects of the gradient of the index of refraction and their combination permits the control of the overall dispersive power.

A GRIN wedge prism with an axial GRIN profile and a curved front surface is illustrated in Figure 3. The necessary chromatic corrections can be accomplished by choosing the axial gradient to function as a diverging lens. The major chromatic effects are canceled between the converging front lens surface and the diverging GRIN rear surface. More general mixed combinations are possible, depending upon the performance and properties required by the optical designer. For example, it is possible to have the front surface shaped as a concave or diverging lens and then have the axial gradient function as a converging lens.

GRIN prisms can be fabricated from a variety of basic compositions. These include plastics, glass compositions, quartz, and fused silica. All of these compositions are available commercially, but are presently limited in the geometries that are available.

THEORETICAL TREATMENT

The following mathematical treatment provides the basics for selecting various prism parameters for a given design. The basic theoretical formulae can be given in exact form, but will be discussed below in the small angle approximation. This will serve to illustrate the general concepts and operation of the invention. These are also meant to demonstrate the general overall parameters and index of refraction profile required for a gradient prism design. Exact calculations of the properties needed to achieve a required performance of such dispersive prisms can be performed by several commercially available optical design software packages. The quantities used in this discussion are defined and illustrated in Figure 5.

Consider a parallel ray entering the prism at a height y from the central optical axis. For an axial GRIN element with planar surfaces whose index varies only in the z direction, the ray passes straight through the prism and exits at the rear tilted surface at the same height y. The value of z at this point is z = Z + y tan A . The refracted angle D(y) is determined by Snell's law, (1) n(z) sin A = sin[A + D(y)] or

(2) D(y) = arcsin[«(z) sin A] - A

All rays that exit the rear face must pass through the (focal) point (F_z , Fy) . The slope, tan D(y), of the ray drawn on Figure 5 A and 5B that exits at (z,y) and passes through this point must satisfy the relation -y F -y

(3) tan D(y) =

F_z - ∑ F_z - L - yta A

This required dependence of D(y) upon y then determines the z dependence of the index profile through equation 1. Figure 5 A depicts a diverging GRIN prism lens which has both F_z and F_y negative. Figure 5B depicts a converging GRIN prism lens which has both F_r and F_y positive.

The dispersive property of the GRIN prism is characterized by the dependence of F_z and F_y on the wave length λ; they in turn depend upon the behavior of the index of refraction upon wave length. The goal of a good design is to have a large dispersion yet to have each wave length sharply focused on the image plane for maximum resolution. The way to make these chromatic corrections can be anticipated by noting that the chromatic changes in the focal length arise from the wave length dependence of the front curved surface and the refraction at the rear surface. If the index profile is chosen so that the rear face acts as a diverging lens, then the index rises from the front to the rear of the prism while its Abbe value decreases. This negative focal length is then combined with the positive focal length from the front surface with its larger Abbe value to produce the total focal length of the system. It will be shown below that the two sources of chromatic shift in the z focal length, F_z , can be arranged to cancel while the dispersion measure, F_y , still depends strongly upon wave length.

The properties of a GRIN prism that has a curved front surface, either spherical or cylindrical in shape, can be conveniently treated analytically. For example, consider the optical element described in Figure 6 whose rear planar surface is inclined at an angle A. The path of a ray incident at a distance y₀ from the optical axis and which focuses at the point (Fz, Fy) can be calculated exactly. However, the essential features can be deduced from an approximate treatment that treats all angles as small. The use of this approximation in the geometric relations and in Snell's law of refraction, in which the sine of an angle is replaced by the angle, leads to the equations:

(4) *. = ^y*/ζ_R , y^ = y₀ ~ Lb(y₀), z = L + Ay_λ ,

(F_z - L)D(L) - y,

D(z_λ ) =

F₂ - z_x

from the geometry, and from the laws of refraction applied at the two surfaces:

(5) b(y0) = ^^ n(z_λ )(A - b(y_Q)) = A + (z, )

«(0) R

The axial index profile is expanded as (6) n(z) - w(0) + n z + n₂z² +...

The above equations give relations between the parameters of the optical system. To first order in the parameter z, , the relations can be written as

(8) F = (F_z - L)A[n(L - 1]

It is well known in the 'thin lens' approximation that the inverse of the focal length of a total system is the sum of the inverses of the focal lengths of the elements that make up the system. In equation (7), (F_z - L) on the left is the focal length of the total GRIN prism system. The first term on the right side is the focal length of the front spherical or cylindrical lens if the rear surface were perpendicular to the optical axis. The second term is the focal length of a GRIN index profile with a surface inclined at an angle A. It is seen that if «, is positive, this acts as a diverging cylindrical lens while if n, is negative, it acts as a converging cylindrical lens. One of the goals of the invention is to provide an optical system that not only disperses the wave length spectrum of the incident light, but also to sharply focus all wave lengths on the image plane. That is, F_z is to be independent of wave length, but F_y is to depend on wave length. To explore this point, consider the derivative of the first of equation (7) with respect to the wave length λ :

₍₁₀₎ s. - * ₊ «£i- _and s_{L =} L_ lL ' ° L n(0f R ^L L W(0) R

It is clear that SQ > S . If n(L) > n(0) , then for standard optical materials, the λ derivative of n(L) is greater than the λ derivative of n(0). Therefore by choosing appropriate values of the parameters, it should be possible to make the λ derivative of F_r , as given in equation (9), vanish. Finally, note that if F_z is independent of wave length, then the transverse dispersion is given by

(11) dλ _{= (F},-_L)A dλ

An alternative design choice is to choose a diverging front surface shape, that is, R < 0, and a decreasing axial index profile. For this parameter set S₀ < S_L , and if the index of refraction increases along the optical axis, F_z can be made to be independent of wave length.

The above approximate treatment holds for an index profile that varies along the optical axis as in Figure 2A. A similar treatment can be given if the profile varies transverse to the optical axis as in Figure 2B. The important point is that the index of refraction varies in a specified way along the rear angled surface of the prism to yield the desired focusing effect. Note however that a transverse index gradient inside the prism also causes a small curvature in the path of the rays. This effect is included in treatments using optical design software. The additional focusing effects of a spherical surface on the front of the prism, such as illustrated in Figure 3, can be treated analytically or also by using optical design software. The spherical or cylindrical surface on the front of the prism can be achieved by using a separate homogeneous lens element such as illustrated in Figures 4 A and 4B. SPECTROGRAPHIC PERFORMANCE

The following designs were done using the ZEMAX optical design program. In the first design, the source was at infinity, the radius of curvature on the front surface was 100mm, the lens diameter was 10mm, and the parameter F, was fixed at 217.6mm. The glass was a lead silicate glass whose dispersive properties were described by Manhart and Pagano.

The total change in F_y of the spectrum over the wave length range 0.45-0.65 microns is 2.683mm. The resolution width in y of a given wave length is approximately 0.012mm. Thus there are roughly 220 resolution cells in this range. The index profile is of the form n(z) = n(0) + H, z + n₂ z ² with n(0) = 1.65, n_λ = 0.032, and n₂ = 0. The length of the top of the prism was 4.173mm, the bottom was 1. 113mm, and tan A = 0.30.

This design is illustrated in Figures 7 A and B for one wave length. A side view of the GRIN prism with its spherical front surface is depicted in Figure 7A. The effect of the GRIN cylindrical diverging lens is seen in Figure 7B. The top view shows the rays converging well in front of the image plane. The side view shows the refraction of the rays by the tilted rear surface and the focusing effect.

In the second design, the source was at a finite distance of 400mm from the front surface. The other parameters were unchanged except that F_z was 663.6mm.

The total change in F_y over the same wave length range is 9.486mm. The resolution width in y of a given wave length is approximately 0.05mm. There are roughly 190 resolution cells in the range. The index profile has n(0) = 1.65, n_x= 0.024, and n₂ = 0. The length of the top of the prism was 4.43mm, the length of the bottom was 0.86mm, and tan A = 0.35.

The maximum index change over the length of the prism is 0.106.

Although examples discussed employ an index gradient oriented along the optical axis, the index gradient may be oriented in any direction desired to achieve the goals of a particular optical design.

The examples illustrated in the figures and discussed above treat the case wherein planes of constant index are oriented orthogonal to the optical axis. This is not the only useful configuration contemplated by the present invention. The primary requirement is that the index profile along the rear, tilted surface be such that the desired focus and dispersion are achieved. In some circumstances this condition may be obtained by tilting the gradient axis with respect to the optical axis. The tilting of the gradient axis has the additional effect of bending the light rays as they transit the interior space of the prism. An optical designer may resort to these additional effects to further improve the device performance. Although the present invention has been described with reference to particular means, materials and embodiments, from the foregoing descriptions, one skilled in the art can ascertain the essential characteristics of the present invention and various changes and modifications may be made to adapt the various uses and characteristics thereof without departing from the spirit and scope of the present invention as set out in the claims which follow.

Claims

WHAT IS CLAIMED IS:

1. An optical prism element for use in an optical system, said prism element comprising: a front curved surface having an optical axis; a rear planar surface angled relative to said optical axis; and said prism having a spatially varying index of refraction.

2. The prism element of claim 1 wherein said spatially varying index of refraction is selected to provide dispersion of an incident light beam.

3. A compound prism, having an optical axis, for use in optical systems and instruments comprising: a first surface comprising a homogeneous front lens with a spherical or cylindrical surface and positive focus, said first surface characterized by a first surface axis; a plane surfaced GRIN prism portion with a second surface opposite said first surface and said second surface tilted with respect to said first surface axis; and said prism having a spatially varying index of refraction.

4. The compound prism of claim 3 wherein said gradient prism portion has its index of refraction varying along the optical axis.

5. The compound prism of claim 3 wherein said gradient prism portion has its index of refraction varying perpendicular to the optical axis.