Non-uniform sampling for unambiguous doppler measurement

1. A method for operating a light detection and ranging (ladar) system, the method comprising:

transmitting, by a laser transmitter, a sequence of laser pulses, each pulse being offset, by a respective time offset of a sequence of time offsets, from a corresponding one of a sequence of uniformly spaced time points;

receiving a sequence of pulses, each received pulse being a reflection of a corresponding pulse of the sequence of transmitted laser pulses from a target;

forming a first array of complex numbers, each corresponding to an amplitude and phase of a received pulse of the sequence of received pulses; and

for each of a plurality of uniformly-spaced test frequencies:

multiplying each of the complex numbers by a corresponding correction factor, of an array of correction factors, to form a second array of complex numbers;

taking a Fourier transform of the second array of complex numbers to form a Fourier array; and

copying a selected element of the Fourier array into a corresponding position in a first corrected spectrum array, the selected element being an element at the test frequency.

2. The method of claim 1 , wherein each correction factor of the array of correction factors is given by exp(−i2πf c ε n ), wherein:

f c is the test frequency, and

ε n is a time offset of the sequence of time offsets.

3. The method of claim 2 , further comprising operating a correlation filter to select the time offset ε n from the sequence of time offsets.

4. The method of claim 1 , wherein the forming of a first array of complex numbers comprises:

mixing the laser pulses of the sequence of laser pulses with a signal from a local oscillator to form an intermediate frequency signal; and

measuring the amplitude and phase of the intermediate frequency signal;

setting the real part of a complex number of the first array of complex numbers to be proportional to a cosine component of the intermediate frequency signal; and

setting the imaginary part of the complex number to be proportional to a sine component of the intermediate frequency signal.

5. The method of claim 1 , wherein the forming of a first array of complex numbers comprises detecting the sequence of received pulses with a Geiger-mode avalanche photodetector.

6. The method of claim 1 , further comprising finding a peak in the first corrected spectrum array and calculating a Doppler velocity of the target from a frequency at which the peak is found.

7. The method of claim 6 , further comprising using the Doppler velocity to intercept the target.

8. The method of claim 1 , wherein the transmitting, by the laser transmitter, of a sequence of laser pulses, comprises using a pseudorandom number generator to generate the sequence of time offsets.

9. The method of claim 1 , wherein the taking of the Fourier transform of the second array of complex numbers comprises taking a fast Fourier transform of the second array of complex numbers.

10. A method for operating a light detection and ranging (ladar) system, the method comprising:

receiving a sequence of laser pulses, each received pulse being a reflection of a corresponding pulse of a sequence of transmitted laser pulses from a target, each of the transmitted pulses being offset, by a respective time offset of a sequence of time offsets, from a corresponding one of a sequence of uniformly spaced time points;

forming a first array of complex numbers, each corresponding to an amplitude and phase of a received pulse of the sequence of received pulses; and

for each of a plurality of uniformly-spaced test frequencies:

forming a convolution of:

a Fourier transform of an array of correction factors; and

a Fourier transform of the first array of complex numbers,

to form a first Fourier array; and

copying a selected element of the first Fourier array into a corresponding position in a first corrected spectrum array, the selected element being an element at the test frequency.

11. The method of claim 10 , wherein each correction factor of the array of correction factors is given by exp(−i2πf c ε n ), wherein:

f c is the test frequency, and

ε n is a time offset of the sequence of time offsets.

12. The method of claim 11 , further comprising operating a correlation filter to select the time offset ε n from the sequence of time offsets.

13. The method of claim 10 , wherein the forming of a first array of complex numbers comprises:

mixing the laser pulses of the sequence of laser pulses with a signal from a local oscillator to form an intermediate frequency signal; and

measuring the amplitude and phase of the intermediate frequency signal;

setting the real part of a complex number of the first array of complex numbers to be proportional to a cosine component of the intermediate frequency signal; and

setting the imaginary part of the complex number to be proportional to a sine component of the intermediate frequency signal.

14. The method of claim 10 , wherein the forming of a first array of complex numbers comprises detecting the sequence of received pulses with a Geiger-mode avalanche photodetector.

15. The method of claim 10 , further comprising finding a peak in the first corrected spectrum array and calculating a Doppler velocity of the target from a frequency at which the peak is found.

16. The method of claim 15 , further comprising using the Doppler velocity to intercept the target.

17. The method of claim 10 , further comprising transmitting, by a laser transmitter, the sequence of laser pulses, wherein the transmitting, by the laser transmitter, of the sequence of laser pulses, comprises using a pseudorandom number generator to generate the sequence of time offsets.

18. The method of claim 10 , wherein the forming of the convolution of:

the Fourier transform of the array of correction factors; and

the Fourier transform of the first array of complex numbers comprises forming the convolution of:

the fast Fourier transform of the array of correction factors; and

the fast Fourier transform of the first array of complex numbers.

19. A ladar system, comprising:

a transmitter;

a receiver; and

a processing unit,

the transmitter being configured to transmit a sequence of laser pulses, each pulse being offset, by a respective time offset of a sequence of time offsets, from a corresponding one of a sequence of uniformly spaced time points,

the receiver being configured to receive a sequence of pulses, each received pulse being a reflection of a corresponding pulse of the sequence of transmitted laser pulses from a target,

the processing unit being configured to:

form a first array of complex numbers, each corresponding to an amplitude and phase of a received pulse of the sequence of received pulses; and

for each of a plurality of uniformly-spaced test frequencies:

multiply each of the complex numbers by a corresponding correction factor, of an array of correction factors, to form a second array of complex numbers;

take a Fourier transform of the second array of complex numbers to form a Fourier array; and

copy a selected element of the Fourier array into a corresponding position in a first corrected spectrum array, the selected element being an element at the test frequency.

20. The system of claim 19 , wherein each correction factor of the array of correction factors is given by exp(−i2πf c ε n ), wherein:

f c is the test frequency, and

ε n is a time offset of the sequence of time offsets.