WAVEFRONT MEASUREMENT

• US 3,694,088 A
• Filed: 01/25/1971
• Issued: 09/26/1972
• Est. Priority Date: 01/25/1971
• Status: Expired due to Term

• Current Assignee: Donald Richard Herriott, John Everett Gallagher
• Original Assignee: Donald Richard Herriott, John Everett Gallagher
• Inventors: Gallagher, John Everett, Herriott, Donald Richard
• Primary Examiner(s): Wibert, Ronald L.
• Assistant Examiner(s): Clark, Conrad
• Application Number:
  US05/109,220
• Time in Patent Office: 610 Days
• Field of Search: 356/106-113
• US Class Current: 356/495
• CPC Class Codes: G01B 2290/40 Non-mechanical variable delay line
• CPC Class Codes: G01B 2290/70 Using polarization in the interferometer
• CPC Class Codes: G01B 9/02011 using temporal polarization variation
• CPC Class Codes: G01B 9/02039 by matching the wavefront with a particular object surface shape
• CPC Class Codes: G01J 9/02 by interferometric methods using interferometers for measuring optically the linear dimensions of objects G01B9/02

Abstract

A conventional interferometer has been modified so that amplitude and phase information contained in an interference pattern may be calculated from intensities read out by a television camera and phase shifts introduced by rotation of a quarter-wave plate. To operate the device, reference light at a first phase is interfered on the television camera with light from the object being tested. Such an object might be a lens. The camera samples the intensity of the interference pattern at an array of points; and these values of intensity are stored in a computer. Next, a known phase shift is introduced into the reference beam by rotating the quarter-wave plate; and the intensity in the resulting interference fringe pattern is again sampled at the same points in the array and stored. This process is again repeated for a second known phase shift. Because the three values of intensity obtained at each point in the array are interrelated by the fact that the intensity at any point in the interferogram is a cosinusoidal function of phase, simultaneous solution at each point of three equations corresponding to the three values of intensity produces phase and amplitude plots of the wavefront from the object under study. Alternatively, by making several measurements of the intensity over phase angles from zero to 2 pi , it is possible to form phase and amplitude plots by determining Fourier coefficients.

Claims

1. A method for measuring at least one of the phase and the amplitude at a point in a wavefront comprising:

forming on a detector at least part of a first interference pattern by interfering thereon the wavefront to be measured and a reference wavefront, there being a first phase relation between said wavefronts;

sampling and measuring the intensity in the first interference pattern at a point in the wavefront to be measured;

changing by a known value the phase relation between the wavefront to be measured and the reference wavefront to a second phase relation;

forming on the detector at least part of a second interference pattern by interfering thereon the wavefront to be measured and the reference wavefront;

sampling and measuring the intensity in the second interference pattern at the same point in the wavefront to be measured; and

determining from the two intensity measurements and the known phase shift at least one of the phase and the amplitude of the wavefront to be measured at the point in that wavefront where the samples were made.

2. The method of claim 1 wherein the intensity is a cosinusoidal function of phase having the general form I Idc + Io cos theta , where I is the intensity measured, Idc is the background intensity, Io is the magnitude of the cosinusoidally varying intensity, and theta is the phase angle.

3. The method of claim 1 wherein the phase and amplitude of the wavefront are determined at the point in the wavefront by the simultaneous solution of equations relating the intensity recorded at each point to the changes in the phase relation between the reference wavefront and the wavefront to be measured.

4. The method of cLaim 1 wherein said method is used to measure the intensity at an array of points in the wavefront to be measured.

5. A method for measuring at least one of the phase and amplitude across a wavefront comprising the steps of:

a. forming on a detector at least part of a first interference pattern by interfering thereon the wavefront to be measured and a reference wavefront, there being a first phase relation between said wavefronts;

b. sampling and measuring the intensity in the first interference pattern at an array of points in the wavefront to be measured;

c. changing by a known value the phase relation between the wavefront to be measured and the reference wavefront to a second phase relation;

d. forming on the detector at least part of a second interference pattern by interfering thereon the wavefront to be measured and the reference wavefront;

e. sampling and measuring the intensity in the second interference pattern at the same array of points in the wavefront to be measured;

f. changing by a known amount the phase relation between the wavefront to be measured and the reference wavefront to a third phase relation;

g. forming on the detector at least part of a third interference pattern by interfering thereon the wavefront to be measured and the reference wavefront;

h. sampling and measuring the intensity in the third interference pattern at the same array of points in the wavefront to be measured; and

i. determining from the values of the intensity recorded at each point and the known changes in the phase relation at least one of the phase and the amplitude of the wavefront to be measured at the points in that wavefront where the samples were made.

6. The method of claim 5 wherein the intensity is a cosinusoidal function of phase having the general form I Idc + Io cos theta , where I is the intensity measured, Idc is the background intensity, Io is the magnitude of the cosinusoidally varying intensity, and theta is the phase angle.

7. The method of claim 6 further comprising the steps of:

repeating steps (a) through (i) of claim 5; and

averaging the values determined by the repetition of steps (a) through (i) with the values first determined by performing steps (a) through (i).

8. The method of claim 7 wherein at least one of the first, second and third phase relations during the repetition of steps (a) through (i) of claim 5 differs from the three phase relations used in first performing steps (a) through (i).

9. The method of claim 7 wherein the phase relations during the first execution of steps (a) through (i) of claim 5 and the repetition of steps (a) through (i) are randomly selected.

10. The method of claim 6 wherein at least one of the phase and the amplitude of the wavefront are determined by:

measuring the intensity recorded at the points in the array for several different values from 0 to 2 pi of the phase relation between the reference wavefront and the wavefront to be measured;

calculating at each point from the relations between the different intensities recorded and the different phases used approximations to a set of Fourier coefficients; and

determining at each point at least one of the phase and the amplitude of the wavefront to be measured from the set of Fourier coefficients for that point.

11. The method of claim 10 wherein at least one of the phase and the amplitude of the wavefront to be measured is determined at the points in the array by:

calculating approximations to the Fourier coefficients L1, L2 and L3 where

12. The method of claim 6 wherein at least one of the phase and the amplitude of the wavefront to be measured is determined by simultaneous solution of the three equations I1 Idc + Io cos ( Alpha ) I2 Idc + Io cos ( Alpha + 1) I3 Idc + Io cos ( Alpha + 2), where I1, I2 and I3 are the three intensities that are measured, Alpha is the phase angle during the formation of the first interference pattern, Alpha + 1 is the phase angle during the formation of the second interference pattern, and Alpha + 2 is the phase angle during the formation of the third interference pattern.

13. Apparatus for measuring at least one of the phase and amplitude across a wavefront comprising:

a television camera tube;

means for interfering on the camera tube a wavefront to be measured and a reference wavefront that have a first phase relation to form signals representative of the intensity in the resulting interference pattern at an array of points on the camera tube;

means for producing known changes in the phase relation between the wavefront to be measured and the reference wavefront to alter the intensity in the interference pattern detected at said array of points on the camera tube; and

means for processing signals representative of the changes in the phase relation and the intensities recorded at each point for at least two different phase relations to determine at least one of the phase and amplitude of the wavefront to be measured at the points in said array.

14. The apparatus of claim 13 wherein the means for processing signals comprises means for solving simultaneously equations relating the intensities detected at each point in said array to the changes in the phase relation.

15. The apparatus of claim 14 wherein the means for processing signals comprises means for solving simultaneously at each point three equations I1 Idc + Io cos ( Alpha ) I2 Idc + Io cos ( Alpha + 1) I3 Idc + Io cos ( Alpha + 2) , where I1, I2 and I3 are three intensities measured at each point in said array for three different interference patterns produced by three different phase relations between the interfering wavefronts, Alpha is the phase angle during the formation of the first interference pattern, Alpha + 1 is the phase angle during the formation of the second interference pattern, and Alpha + 2 is the phase angle during the formation of the third interference pattern.

16. The apparatus of claim 13 wherein the means for processing signals comprises means for calculating a set of Fourier coefficients for each point in said array, from the different intensities recorded and the changes in the phase relation.

17. The apparatus of claim 16 wherein the means for processing signals comprises:

means for calculating approximations to the Fourier coefficients L1, L2 and L3 where means for determining Idc, Io and Alpha from the relations Idc L1/2 pi Io (L22 + L32) 1/2 / pi Alpha arc tan (-L2/L3), where Alpha is the phase angle during the formation of the first interference pattern; and

means for determining from the values for Idc, Io and Alpha at each point at least one of the phase and the amplitude of the wavefront to be measured.