Method of calibrating an interferometer and reducing its systematic noise

• US 5,675,513 A
• Filed: 02/16/1996
• Issued: 10/07/1997
• Est. Priority Date: 02/16/1996
• Status: Expired due to Fees

• Current Assignee: Administrator of The National Aeronautics and Space Administration
• Original Assignee: United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration
• Inventors: Hammer, Philip D.
• Primary Examiner(s): Voeltz, Emanuel T.
• Assistant Examiner(s): MILLER, CRAIG S
• Application Number:
  US08/605,348
• Time in Patent Office: 599 Days
• Field of Search: 356/345, 356/349, 356/376, 250/252.1, 364/571.02, 364/525, 364/526, 364/560, 364/523, 364/577, 364/575
• US Class Current: 702/86
• CPC Class Codes: G01B 9/02074 of the detector
• CPC Class Codes: G01B 9/02084 Processing in the Fourier or frequency domain when not imaged in the frequency domain
• CPC Class Codes: G01J 9/02 by interferometric methods using interferometers for measuring optically the linear dimensions of objects G01B9/02

Abstract

Methods of operation and data analysis for an interferometer so as to eliminate the errors contributed by non-responsive or unstable pixels, interpixel gain variations that drift over time, and spurious noise that would otherwise degrade the operation of the interferometer are disclosed. The methods provide for either online or post-processing calibration. The methods apply prescribed reversible transformations that exploit the physical properties of interferograms obtained from said interferometer to derive a calibration reference signal for subsequent treatment of said interferograms for interpixel gain variations. A self-consistent approach for treating bad pixels is incorporated into the methods.

Claims

1. A method of operating an interferometer having means to process light from a light source to produce an interferogram corresponding to an image of a target, having a range of fringe path differences, onto a focal plane and having means to image a field of view of said interferometer on a frame set basis onto a detector having pixels which provide signals to form a first illumination pattern also corresponding to said image of said target and having unwanted components and comprising an interferogram frame set having m, n and l dimensions serving as coordinates of the interferogram frame sets, said method removing unwanted components of said first illumination pattern and comprising the steps of:

(a) accepting an interferogram frame set containing pixel information;

(b) averaging the pixel information of said interferogram over the l dimension thereof to yield a single, coadded interferogram frame having only m and n dimensions;

(c) normalizing said coadded interferogram frame to reduce signal variations along spatial coordinates thereof;

(d) detecting bad pixel information of said normalized coadded interferogram frame;

(e) interpolating for first bad pixel information so as to remove said bad pixel information from said coadded interferogram frame;

(f) applying phase alignment correction to the interpolated, coadded interferogram frame so as to remove said unwanted components from said first illumination pattern;

(g) filtering said phase alignment corrected interferogram frame to develop a systematic noise frame;

(h) applying an inverse phase alignment correction to said systematic noise frame to develop a second order calibration frame;

(i) re-accepting one of same and similar interferogram frame sets;

(j) applying at least said second calibration frame to said re-accepted interferogram frame set of step (i) to correct for inter-pixel gain variation systematic errors so as to remove said inter-pixel gain variation systematic errors from said re-accepted interferogram frame set;

(k) normalizing said inter-pixel gain variation corrected interferograms;

(l) interpolating for second bad pixel information so as to remove said bad pixel information from said normalized inter-pixel gain variation corrected interferograms;

(m) applying inverse normalization to said interpolated, inter-pixel gain variation corrected interferograms to form second order corrected interferogram frame; and

(n) collecting the results of steps (j) through (m) repeated over the index 1 to yield second order corrected interferogram data frame set having m,n,l dimensions and serving as a second illumination pattern corresponding to said image of said target but being transformed from said first illumination pattern so that said image of said target has said unwanted components removed therefrom as well as being free of said first and second bad pixel information and said inter-pixel gain variation systematic errors.

2. The method of operating an interferometer according to claim 1 further comprising the steps of:

(a) applying a calibration reference measurement to the averaged pixel information of step (b) of claim 1 before the averaged pixel information is normalized in step (c) of claim 1; and

(b) applying said calibration reference measurement to said re-accepted first interferogram along with said second calibration frame in step (j) of claim 1 for said correction of said inter-pixel gain variations systematic errors.

3. A method of operating an interferometer having means to process light from a light source to produce an interferogram corresponding to an image of a target, having a range of fringe path differences, onto a focal plane and having means to image a field of view of said interferometer on a frame set basis as an interferogram frame of a detector to form a first illumination pattern also corresponding to said image of said target and having unwanted components, said detector comprising pixels arranged into a m, n, l matrix defining the coordinates of said interferogram frame, each of said interferogram frames serving as raw data of said illumination pattern represented by signals associated with said pixels, said method removing unwanted components of said first illumination pattern and comprising the steps of:

(a) accepting an interferogram frame set containing pixel information;

(b) averaging the pixel information of said interferogram over the l dimension thereof to yield an interferogram frame having only m and n dimensions;

(c) normalizing said averaged interferogram frame;

(d) detecting first bad pixel information of said normalized interferogram frame;

(e) interpolating for the bad pixel information so as to remove said first bad pixel information from said normalized interferogram;

(f) performing phase alignment correction on said interpolated and normalized interferogram and deriving row-wise phase coefficients and a data frame in which the interferogram frames are symmetric about a zero phase difference (ZPD) quantity and are aligned along all of said n dimension so as remove said unwanted components of said first illumination pattern;

(g) storing said row-wise phase coefficients;

(h) performing a two-dimensional transform on the data frame in which the interferogram frame is symmetric about said zero phase difference so that said data frame is transformed from being a real signal into its elementary complex components;

(i) filtering said transformed data frame to separate systematic noise therefrom;

(j) performing an inverse composite two-dimensional (2D) transform on said systematic noise;

(k) combining said stored row-wise phase coefficients with said inverse two-dimensional transformed systematic noise to derive a second order pixel gain variation frame G2;

(l) re-accepting said interferogram frame set containing pixel information;

(m) sequentially selecting said accepted interferogram frame of step (1) over the l dimension thereof;

(n) normalizing said sequentially selected interferogram frame;

(o) detecting second bad pixel information of said normalized and sequentially selected interferogram frame;

(p) interpolating for the second bad pixel information so as to remove said second bad pixel information from said normalized and sequentially selected interferogram frame;

(q) performing inverse normalization of the normalized data of step (p) to form a second order corrected frame D2;

(r) accepting a second interferogram frame by step (m) and repeating steps (n)-(q); and

(s) continuing step (r) for all of the frames of the raw data comprising said image and collecting the resulting corrected interferogram frame set having m,n,l dimensions and serving as a second illumination pattern corresponding to said image of said target but being transformed from said first illumination pattern so that said target has said unwanted components removed therefrom as well as being free of said first and second bad pixel information.

4. The method of operating an interferometer according to claim 3 further comprising the steps of:

(a) dividing a calibration reference measurement into the averaged pixel information of step (b) of claim 3 before the average pixel information is normalized in step (c) of claim 3; and

(b) dividing the summation of a calibration reference measurement and said second order pixel gain variation frame G2 into said sequence checked interferogram frame of said step (m) of claim 3 before said sequence checked interferogram frame is normalized in said step (n) of claim 3.