Adaptively determining the sign in a fringe count detection system

1. A method of extracting phase due to fringe count error (FCE) in spectra formed by an interferometer, comprising the steps of:

(a) forming an earth scene spectrum

(b) forming a background reference spectrum;

(c) forming a phase extraction function, R k , where k is a k th channel of the interferometer, using the formed earth scene spectrum and the background spectrum;

(d) using recursive least squares (RLS) to extract phase from the R k function, and

(e) providing the extracted phase to a user to correct the FCE.

2. The method of claim 1 , wherein

step (c) includes forming a term in the R k function that includes a positive or a negative sign of a square root; and

step (d) includes determining whether the sign is negative or positive using the RLS.

3. The method of claim 2 , wherein step (d) includes

extrapolating a phase at channel k to a phase at channel k+1 using the RLS,

determining a first phase at channel k+1 resulting from using a positive sign of the square root in the phase extraction function,

determining a second phase at channel k+1 resulting from using a negative sign of the square root in the phase extraction function, and

selecting one of the determined first or second phase at channel k+1, based on the determined first or second phase that minimizes an absolute error to the extrapolated phase.

4. The method of claim 2 , wherein step (d) includes

determining at least one value of phase at a first frequency, where the first frequency is a frequency operating at channel k=0 of the interferometer; and

extrapolating the determined value of phase to a next frequency operating at channel k=1 of the interferometer.

5. The method of claim 4 , wherein extrapolating the determined value of phase, includes

determining a first value of phase at channel k=0 assuming a positive sign in the square root of the phase extraction function and extrapolating the first value of phase to a next channel, k=1, of the interferometer; and

determining a second value of the phase at channel k=0 assuming a negative sign in the square root of the phase extraction function and extrapolating the second value of phase to the next channel, k=1, of the interferometer.

6. The method of claim 5 , wherein

extrapolating the first and second value of phases includes performing a separate RLS over a bandwidth of k frequencies to obtain, respectively, first and second sets of adaptive phases, and

selecting one of the first and second sets of adaptive phases that satisfies a predetermined rule.

7. The method of claim 6 , wherein selecting one of the first and second sets of adaptive phases includes

selecting one of the first or second sets of adaptive phases that satisfies the following equality:

[the sign of a median phase in the set of adaptive phases]=[the sign of a mean phase slope in the set of adaptive phases].

8. The method of claim 1 , wherein

step (d) includes using the RLS to determine a line having a positive or negative slope, where the line represents phases at k frequencies, and the slope of the line represents a number of fringe errors.

9. The method of claim 8 , wherein

the number of fringe errors is proportional to the slope of the line, and a horizontal line represents no fringe error.

10. The method of claim 1 , wherein forming the spectra in steps (a) and (b) includes

obtaining interferograms, and

performing a fast Fourier transform (FFT) on each of the interferograms to obtain a respective spectrum.

11. In a phase extraction function of an interferometer at channel number k, where the phase extraction function includes a square root sign that is either positive or negative,

a method of determining whether the sign is positive or negative, comprising the steps of:

RLS-computing a first set of phases as a function of channel number k, using the phase extraction function, assuming a positive square root sign beginning at k=0;

RLS-computing a second set of phases as a function of channel number k, using the phase extraction function, assuming a negative square root sign beginning at k=0; and

selecting the first or second set of phases based on a predetermined rule; and

providing the selected first or second set of phases to a user for correcting fringe count errors (FCE) of the interferometer.

12. The method of claim 11 , wherein

selecting the first or second set of phases is based on the following sub-steps:

separately determining a sign of a median phase in the first and second sets of phases;

separately determining a sign of a mean phase slope in the first and second sets of phases; and

selecting the first or second set of phases satisfying the following equality:

the sign of the median phase=the sign of the mean phase slope.

13. The method of claim 11 , wherein RLS-computing includes

extrapolating phase from channel k to channel k+1, assuming a positive square root sign;

extrapolating phase from channel k to channel k+1, assuming a negative square root sign; and

selecting the extrapolated phase in channel k+1 that minimizes an absolute error to the extrapolated phase.

14. The method of claim 11 , wherein

the RLS-computing includes calculating phase values as a function of frequency,

wherein the phase values as a function of frequency is a straight line plotted on X,Y axes having a Y-intercept at k=0.

15. The method of claim 11 , wherein

the phase extraction function includes earth scene, and calibration spectra.

16. A computer for executing an algorithm for determining fringe count error (FCE) of an interferometer comprising the steps of:

forming a phase extraction function from earth scene and calibration spectra, where the phase extraction function varies with frequency and includes a square root sign that is either positive or negative at each frequency; and

determining whether the square root sign is positive or negative at each frequency using an RLS method.

17. The computer of claim 16 , including the steps of:

letting the square root sign be positive at a starting frequency, and calculating a first set of phases as a function of frequency;

letting the square root sign be negative at the starting frequency, and calculating a second set of phases as a function of frequency; and

selecting the first or second set of phases based on a predetermined rule.

18. The computer of claim 17 , wherein

selecting the first or second set of phases is based on satisfying the following equality for each set of phases:

sign of the median phase=sign of the mean phase slope.

19. The computer of claim 16 , wherein using the RLS method includes

extrapolating phase from frequency k to frequency k+1, assuming a positive square root sign;

extrapolating phase from frequency k to frequency k+1, assuming a negative square root sign; and

selecting the extrapolated phase at frequency k+1 that minimizes an absolute error to the extrapolated phase.

20. The computer of claim 16 , including

correcting the FCE using an FCE correction algorithm.