Systems and methods for interferometric phase measurement

1. A method for measuring phase shift to detect irregularities of a surface, said method is implemented with a camera, a computing device coupled to or within the camera, a light source, a surface disposed opposite the light source, a semi-reflective reference plane disposed between the light source and the surface, and a beam splitter disposed between the light source and the reference plane, wherein the light source emits a light beam comprising a first portion and a second portion, wherein the first portion is reflected by the reference plane and the second portion is transmitted through the reference plane and reflected by the surface, wherein the beam splitter directs the reflected first portion and the reflected second portion to the camera, said method comprising the steps of:

generating a first image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along a distance between the surface and the beam splitter at a first phase sweep rate;

generating a second image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along the distance at a second phase sweep rate;

generating a third image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along the distance at a third phase sweep rate;

generating, by the computing device, a first Fourier transform image and a second Fourier transform image based on the first image, the second image, and the third image; and

generating, by the computing device, a phase image based on the first Fourier transform image and the second Fourier transform image.

2. The method of claim 1 , wherein translating the reference plane along a distance further comprises translating the reference plane along a distance that corresponds to a phase sweep that is an integer multiple of 2*pi radians.

3. The method of claim 1 , wherein generating the first Fourier transform image comprises subtracting the first image from the second image.

4. The method of claim 1 , wherein generating the second Fourier transform image comprises subtracting the first image from the third image.

5. The method of claim 1 , wherein generating the phase image comprises calculating an arctangent of the second Fourier transform image divided by the first Fourier transform image.

6. The method of claim 1 , further comprising controlling the first phase sweep rate such that the first phase sweep rate is constant and the camera accumulates a first phase-dependent fringe intensity.

7. The method of claim 6 , further comprising controlling the second phase sweep rate such that the camera accumulates a second phase-dependent fringe intensity that is equal to the first phase-dependent fringe intensity plus a first order cosine Fourier transform of the first phase-dependent fringe intensity.

8. The method of claim 6 , further comprising controlling the third phase sweep rate such that the camera accumulates a third phase-dependent fringe intensity that is equal to the first phase-dependent fringe intensity plus a first order sine Fourier transform of the first phase-dependent fringe intensity.

9. A system for measuring phase shift to detect irregularities of a surface, said system comprising:

a camera;

a computing device coupled to or within the camera;

a light source;

a surface disposed opposite the light source;

a semi-reflective reference plane disposed between the light source and the surface; and

a beam splitter disposed between the light source and the reference plane, wherein the light source emits a light beam comprising a first portion and a second portion, wherein the first portion is reflected by the reference plane and the second portion is transmitted through the reference plane and reflected by the surface, wherein the beam splitter directs the reflected first portion and the reflected second portion to the camera, and wherein said system is configured to:

generate a first image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along a distance between the surface and the beam splitter at a first phase sweep rate;

generate a second image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along the distance at a second phase sweep rate;

generate a third image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along the distance at a third phase sweep rate;

generate a first Fourier transform image and a second Fourier transform image based on the first image, the second image, and the third image; and

generate a phase image based on the first Fourier transform image and the second Fourier transform image.

10. The system of claim 9 , wherein the surface is a surface of a wafer.

11. The system of claim 9 , wherein said system is further configured to translate the reference plane along a distance by translating the reference plane along a distance that corresponds to a phase sweep that is an integer multiple of 2*pi radians.

12. The system of claim 9 , wherein said system is further configured to generate the first Fourier transform image by subtracting the first image from the second image.

13. The system of claim 9 , wherein said system is further configured to generate the second Fourier transform image by subtracting the first image from the third image.

14. The system of claim 9 , wherein said system is further configured to generate the phase image by calculating an arctangent of the second Fourier transform image divided by the first Fourier transform image.

15. The system of claim 9 , wherein said system is further configured to control the first phase sweep rate such that the first phase sweep rate is constant and the camera accumulates a first phase-dependent fringe intensity.

16. The system of claim 15 , wherein said system is further configured to control the second phase sweep rate such that the camera accumulates a second phase-dependent fringe intensity that is equal to the first phase-dependent fringe intensity plus a first order cosine Fourier transform of the first phase-dependent fringe intensity.

17. The system of claim 15 , wherein said system is further configured to control the third phase sweep rate such that the camera accumulates a third phase-dependent fringe intensity that is equal to the first phase-dependent fringe intensity plus a first order sine Fourier transform of the first phase-dependent fringe intensity.

18. A non-transitory computer-readable storage medium having computer-executable instructions embodied thereon for measuring phase shift to detect irregularities of a surface in a system including a camera, a computing device coupled to or within the camera, a light source, a surface disposed opposite the light source, a semi-reflective reference plane disposed between the light source and the surface, and a beam splitter disposed between the light source and the reference plane, wherein the light source emits a light beam comprising a first portion and a second portion, wherein the first portion is reflected by the reference plane and the second portion is transmitted through the reference plane and reflected by the surface, and wherein the beam splitter directs the reflected first portion and the reflected second portion to the camera, wherein when executed by the computing device, said computer-executable instructions cause the computing device to:

generate a first image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along a distance between the surface and the beam splitter at a first phase sweep rate;

generate a second image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along the distance at a second phase sweep rate;

generate a third image by exposing the camera to the first portion and the second portion of the light beam while translating the reference plane along the distance at a third phase sweep rate;

generate a first Fourier transform image and a second Fourier transform image based on the first image, the second image, and the third image; and

generate a phase image based on the first Fourier transform image and the second Fourier transform image.

19. The non-transitory computer-readable storage medium of claim 18 , further comprising computer-executable instructions that, when executed by the computing device, cause the computing device to translate the reference plane along a distance by translating the reference plane along a distance that corresponds to a phase sweep that is an integer multiple of 2*pi radians.

20. The non-transitory computer-readable storage medium of claim 18 , further comprising computer-executable instructions that, when executed by the computing device, cause the computing device to generate the first Fourier transform image by subtracting the first image from the second image and to generate the second Fourier transform image by subtracting the first image from the third image.