Optical systems employing stepped diffractive surfaces

• US 6,262,844 B1
• Filed: 08/27/1999
• Issued: 07/17/2001
• Est. Priority Date: 08/28/1998
• Status: Expired due to Fees

• Current Assignee: KSM Associates, Inc.
• Original Assignee: KSM Associates, Inc.
• Inventors: Soskind, Yakov G.
• Primary Examiner(s): HENRY, JON W
• Application Number:
  US09/384,819
• Time in Patent Office: 690 Days
• Field of Search: 359/565, 359/569, 359/570, 359/572, 359/15, 359/16, 359/19
• US Class Current: 359/565
• CPC Class Codes: G02B 27/0037 with diffracting elements G02B27/0056 takes precedence; holographic optical elements G02B5/32; zone systems G02B5/1876
• CPC Class Codes: G02B 27/4205 having a diffractive optical element [DOE] contributing to image formation, e.g. whereby modulation transfer function MTF or optical aberrations are relevant
• CPC Class Codes: G02B 27/4211 correcting chromatic aberrations G02B27/0056, G02B27/4222, G02B27/4227 take precedence
• CPC Class Codes: G02B 27/4216 correcting geometrical aberrations
• CPC Class Codes: G02B 27/4222 in projection exposure systems, e.g. photolithographic systems
• CPC Class Codes: G02B 27/4266 Diffraction theory; Mathematical models
• CPC Class Codes: G02B 27/4283 having a diffractive element with major temperature dependent properties
• CPC Class Codes: G02B 5/1814 structurally combined with one or more further optical elements, e.g. lenses, mirrors, prisms or other diffraction gratings G02B5/189 takes precedence
• CPC Class Codes: G02B 5/1876 Diffractive Fresnel lenses; Zone plates; Kinoforms G02B5/1842, G02B5/1847 take precedence; optical systems having diffractive correction means G02B27/0037; Fresnel lenses operating by refraction G02B3/08
• CPC Class Codes: G02B 5/1895 such optical elements having dioptric power
• CPC Class Codes: Y10S 359/90 Methods

Abstract

Stepped diffractive surfaces (13) are used to reduce variations in the optical properties of an optical system as a result of a change in the temperature of all or a portion of the system. Such surfaces have optothermal coefficients which differ from the optothermal coefficients of both kinoforms and refractive elements. Accordingly, stepped diffractive surfaces can be combined with such elements to achieve overall thermal control of optical systems employing such elements.

Claims

1. A method for at least partially controlling a change in an optical property of an optical system resulting from a change in the temperature of at least a portion of the system, said system having an optical axis and comprising at least one lens element having an index of refraction, a shape, and a location within the optical system, said method comprising:

(A) including at least one stepped diffractive surface in the system, said at least one stepped diffractive surface comprising N concentric planar zones which;

(i) are orthogonal to the system'"'"'s optical axis,

(ii) are displaced from one another along the optical axis, the displacement between zone i and zone i+1 being d_i, and

(iii) define a base curve, said stepped diffractive surface having a clear aperture and a sag which changes monotonically from the optical axis to the clear aperture; and

(B) selecting the base curve and the d_i at least in part to compensate for a change in the index of refraction, shape, and/or location of said at least one lens element as a result of said change in temperature to at least partially control the change in the optical property.

3. The method of claim 1 or 2 wherein the optical system forms an image of an object and the optical property is the location of the image along the optical axis.

4. The method of claim 1 or 2 wherein the optical system has a focal length and the optical property is the magnitude of the focal length.

5. The method of claim 1 or 2 wherein the optical system has a magnification and the optical property is the magnitude of the magnification.

6. The method of claim 1 or 2 wherein the at least one lens element has a non-zero optical power and the base curve and the d_i are selected at least in part to compensate for a change in said non-zero optical power resulting from a change in the temperature of said at least one lens element.

7. The method of claim 1 or 2 wherein the optical system includes a housing and the base curve and the d_i are selected at least in part to compensate for a change in the location of the at least one lens element caused by a change in a dimension of said housing resulting from a change in the temperature of the housing.

8. The method of claim 1 wherein:

(a) the optical system has a nominal operating wavelength λ

₀;

(b) the stepped diffractive surface;

(i) separates a first medium having an index of refraction n₁ from a second medium having an index of refraction n₂,

(ii) is formed of a material having an expansion coefficient α

,

(iii) has a base curve of radius R₀ at the optical axis, and

(iv) undergoes a change in temperature Δ

T; and

(c) the base curve and the d_i are selected at least in part based on the equations;

$\begin{array}{c}{\mathrm{\Delta <br><br>\Phi <br><br>}}_{\mathrm{SDS}}={\mathrm{\Phi <br><br>}}_{\mathrm{SDS}}^{\mathrm{Eff}}·<br><br>X_{\mathrm{\Phi <br><br>},\mathrm{SDS}}·<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>T;<br><br>\\ {\mathrm{\Phi <br><br>}}_{\mathrm{SDS}}^{\mathrm{Eff}}=-\frac{\left(n_2-n_1\right)}{R_0};<br><br>\mathrm{and}\\ X_{\mathrm{\Phi <br><br>},\mathrm{SDS}}=\frac{1}{\left(n_2-n_1\right)}<br><br>\left(\frac{<br><br>n_1}{<br><br>T}-\frac{<br><br>n_2}{<br><br>T}\right)-\mathrm{\alpha <br><br>}\end{array}$

where Δ

Φ

_SDS is the change in the paraxial optical power of the stepped diffractive surface at λ

₀ as a result of the change in temperature Δ

T.

10. The method of claim 1 or 2 wherein:

11. The method of claim 1 or 2 wherein:

23. The method of claim 1 or 2 wherein:

(1) the optical system comprises at least one optical surface which (i) is not a stepped diffractive surface and (ii) has a non-zero optical power, said at least one optical surface having at least one monochromatic aberration (the non-SDS aberration);

(2) the at least one stepped diffractive surface has at least one monochromatic aberration (the SDS aberration); and

(3) the non-SDS aberration and the SDS aberration are substantially balanced against one another.

2. A method for at least in part controlling a change in an optical property of an optical system resulting from a change in the temperature of at least a portion of the system, said system having an optical axis and a nominal operating wavelength λ

₀, and comprising at least one lens element having an index of refraction, a shape, and a location within the optical system, said method comprising;

(A) including at least one stepped diffractive surface in the system, said at least one stepped diffractive surface;

(i) separating a first medium having an index of refraction n₁ from a second medium having an index of refraction n₂;

(ii) having a working diffractive order “

j”

which may be constant or variable; and

(iii) comprising N concentric planar zones orthogonal to the system'"'"'s optical axis which define a base curve, said zones satisfying the relationship;

9. The method of claim 2 wherein:

(a) the stepped diffractive surface;

(i) is formed of a material having an expansion coefficient α

,

(ii) has a base curve of radius R₀ at the optical axis, and

(iii) undergoes a change in temperature Δ

T; and

(b) the base curve and the d_i are selected at least in part based on the equations;

$\begin{array}{c}{\mathrm{\Delta <br><br>\Phi <br><br>}}_{\mathrm{SDS}}={\mathrm{\Phi <br><br>}}_{\mathrm{SDS}}^{\mathrm{Eff}}·<br><br>X_{\mathrm{\Phi <br><br>},\mathrm{SDS}}·<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>T;<br><br>\\ {\mathrm{\Phi <br><br>}}_{\mathrm{SDS}}^{\mathrm{Eff}}=-\frac{\left(n_2-n_1\right)}{R_0};<br><br>\mathrm{and}\\ X_{\mathrm{\Phi <br><br>},\mathrm{SDS}}=\frac{1}{\left(n_2-n_1\right)}<br><br>\left(\frac{<br><br>n_1}{<br><br>T}-\frac{<br><br>n_2}{<br><br>T}\right)-\mathrm{\alpha <br><br>}\end{array}$

where Δ

Φ

_SDS is the change in the paraxial optical power of the stepped diffractive surface at λ

₀ as a result of the change in temperature Δ

T.

12. An optical system which has an optical axis and an operating temperature within a range of temperatures, said system comprising:

(a) at least one stepped diffractive surface which comprises N concentric planar zones which;

(i) are orthogonal to the system'"'"'s optical axis,

(ii) are displaced from one another along the optical axis, the displacement between zone i and zone i+1 being d_i, and

(iii) define a base curve, said stepped diffractive surface having a clear aperture and a sag which changes monotonically from the optical axis to the clear aperture;

(b) at least one optical surface which (i) is not a stepped diffractive surface and (ii) has a non-zero optical power; and

(c) a housing which supports the at least one stepped diffractive surface and the at least one optical surface;

wherein the at least one stepped diffractive surface compensates for changes in the at least one optical surface and/or the housing as a result of changes in the system'"'"'s operating temperature.

14. The optical system of claim 12 or 13 wherein the at least one optical surface comprises a refractive surface.

15. The optical system of claim 12 or 13 wherein the at least one optical surface comprises a kinoform.

16. The optical system of claim 12 or 13 wherein the at least one optical surface comprises a reflective surface.

17. The optical system of claim 12 wherein:

(a) the optical system has a nominal operating wavelength λ

₀;

(b) the stepped diffractive surface;

(i) separates a first medium having an index of refraction n₁ from a second medium having an index of refraction n₂,

(ii) is formed of a material having an expansion coefficient α

,

(iii) has a base curve of radius R₀ at the optical axis, and

(iv) undergoes a change in temperature Δ

T; and

(c) the base curve and the d_i are selected at least in part based on the equations;

$\begin{array}{c}{\mathrm{\Delta <br><br>\Phi <br><br>}}_{\mathrm{SDS}}={\mathrm{\Phi <br><br>}}_{\mathrm{SDS}}^{\mathrm{Eff}}·<br><br>X_{\mathrm{\Phi <br><br>},\mathrm{SDS}}·<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>T;<br><br>\\ {\mathrm{\Phi <br><br>}}_{\mathrm{SDS}}^{\mathrm{Eff}}=-\frac{\left(n_2-n_1\right)}{R_0};<br><br>\mathrm{and}\\ X_{\mathrm{\Phi <br><br>},\mathrm{SDS}}=\frac{1}{\left(n_2-n_1\right)}<br><br>\left(\frac{<br><br>n_1}{<br><br>T}-\frac{<br><br>n_2}{<br><br>T}\right)-\mathrm{\alpha <br><br>}\end{array}$

where Δ

Φ

_SDS is the change in the paraxial optical power of the stepped diffractive surface at λ

₀ as a result of the change in temperature Δ

T.

19. The optical system of claim 12 or 13 wherein:

20. The method of claim 12 or 13 wherein:

24. The optical system of claim 12 or 13 wherein:

(1) the at least one optical surface which is not a stepped diffractive surface and has a non-zero optical power has at least one monochromatic aberration (the non-SDS aberration);

(2) the at least one stepped diffractive surface has at least one monochromatic aberration (the SDS aberration); and

(3) the non-SDS aberration and the SDS aberration are substantially balanced against one another.

13. An optical system which (i) has an optical axis, (ii) has a nominal operating wavelength λ

₀, and (iii) has an operating temperature within a range of temperatures, said system comprising;

(a) at least one stepped diffractive surface which;

(i) separates a first medium having an index of refraction n₁ from a second medium having an index of refraction n₂;

(ii) has a working diffractive order “

j”

which may be constant or variable; and

(iii) comprises N concentric planar zones orthogonal to the system'"'"'s optical axis which define a base curve, said zones satisfying the relationship;

18. The optical system of claim 13 wherein:

(a) the stepped diffractive surface;

(i) is formed of a material having an expansion coefficient α

,

(ii) has a base curve of radius R₀ at the optical axis, and

(iii) undergoes a change in temperature Δ

T; and

(b) the base curve and the d_i are selected at least in part based on the equations;

$\begin{array}{c}{\mathrm{\Delta <br><br>\Phi <br><br>}}_{\mathrm{SDS}}={\mathrm{\Phi <br><br>}}_{\mathrm{SDS}}^{\mathrm{Eff}}·<br><br>X_{\mathrm{\Phi <br><br>},\mathrm{SDS}}·<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>T;<br><br>\\ {\mathrm{\Phi <br><br>}}_{\mathrm{SDS}}^{\mathrm{Eff}}=-\frac{\left(n_2-n_1\right)}{R_0};<br><br>\mathrm{and}\\ X_{\mathrm{\Phi <br><br>},\mathrm{SDS}}=\frac{1}{\left(n_2-n_1\right)}<br><br>\left(\frac{<br><br>n_1}{<br><br>T}-\frac{<br><br>n_2}{<br><br>T}\right)-\mathrm{\alpha <br><br>}\end{array}$

where Δ

Φ

_SDS is the change in the paraxial optical power of the stepped diffractive surface at λ

₀ as a result of the change in temperature Δ

T.

21. An optical element comprising two optical surfaces wherein:

(a) one of the optical surfaces comprises a stepped diffractive surface formed in a substrate, said stepped diffractive surface having an optothermal coefficient which depends on dn/dT, where n is the index of refraction of the substrate and T is temperature;

(b) the other of the optical surfaces (i) is not a stepped diffractive surface and (ii) has a non-zero optical power;

(c) the stepped diffractive surface compensates for changes in the other optical surface as a result of changes in the element'"'"'s temperature; and

(d) at a nominal wavelength λ

₀, the stepped diffractive surface has zero paraxial power.

22. The optical element of claim 21 wherein the element has an optical power and the compensation holds said optical power substantially constant over a predetermined range of temperatures for at least one operating wavelength.

25. The optical element of claim 21 wherein the stepped diffractive surface compensates only for changes in the other optical surface as a result of changes in the element'"'"'s temperature.