Techniques for recovering optical spectral features using a chirped optical field

1. A method for recovering optical spectral features using a chirped optical field, comprising the steps of:

receiving a detected time series that represents a temporally varying intensity of an optical signal in response to an interaction between a target optical spectrum and a chirped optical field, wherein

the chirped optical field is an optical field that has a monochromatic frequency that varies in time, and

the target optical spectrum in an optical frequency dependent optical property of a material or device;

determining a phase correction factor based only on one or more properties of the chirped optical field; and

correcting the detected time series based on the phase correction factor to produce an output time series that reproduces in time a shape of the target spectrum in frequency.

2. A method as recited in claim 1 , said step of determining the phase correction factor further comprising determining the phase correction factor based on a quadratic phase term.

3. A method as recited in claim 1 , wherein:

the chirped optical field has a plurality of well-known values for a corresponding plurality of well-known properties; and

said step of determining the phase correction factor further comprising determining the phase correction factor based on the well-known values.

4. A method as recited in claim 3 , wherein the plurality of well-known properties include:

a constant chirp rate (κ) that indicates a change in frequency of the chirped optical field with time, and

a start frequency (νs) that indicates an initial frequency at a start of the chirped optical field.

5. A method as recited in claim 4 , said step of determining the phase correction factor further comprising determining a frequency (ν) dependent correction factor based on a chirped phase term φc given by the equation

ti φ c=exp[i π(2 νsν−ν 2 )/κ]

that includes an effect of a quadratic phase, where i is the square root of −1 and π is the well known ratio of a circumference to a diameter.

6. A method as recited in claim 5 , said step of correcting the detected time series based on the phase correction factor further comprising:

determining a Fourier transform of the detected time series;

multiplying the Fourier transform of the detected time series by the correction factor equal to the reciprocal of the phase term φc to produce a corrected transform; and

determining an inverse Fourier transform of the corrected transform to produce the output time series.

7. A method as recited in claim 5 , said step of correcting the detected time series based on the phase correction factor further comprising:

determining an inverse Fourier transform of the correction factor equal to the reciprocal of the phase term φc to produce a transformed correction; and

convolving the transformed correction with the detected time series to produce the output time series.

8. A method as recited in claim 1 , said step of determining the phase correction factor further comprising determining a Fourier transform of the chirped optical field.

9. A method as recited in claim 8 , said step of correcting the detected time series based on the phase correction factor further comprising:

determining a Fourier transform of the detected time series;

multiplying the Fourier transform of the detected time series by the correction factor proportional to the reciprocal of the Fourier transform of the chirped optical field to produce a corrected transform; and

determining an inverse Fourier transform of the corrected transform to produce the output time series.

10. A method as recited in claim 1 , said step of receiving a detected time series further comprising receiving a detected time series that represents a temporally varying intensity of an optical signal in response to an interaction between a chirped reference optical field and a response signal, wherein:

the response signal is due to the interaction of the target optical spectrum and the chirped optical field, and

the chirped reference optical field is selected to produce a detectable heterodyne signal at an optical detector.

11. A method for recovering optical spectral features using a chirped optical grating, comprising the steps of:

receiving a detected time series that represents a temporally varying intensity of an optical signal in response to an interaction between an incident optical field having a target optical spectrum and a material with a chirped spectral grating, wherein the chirped spectral grating is a spectral grating of grating period that varies with optical frequency, and

determining a phase correction factor based only on one or more properties of the chirped spectral grating; and

correcting the detected time series based on the phase correction factor to produce an output time series that reproduces in time a shape of the target spectrum in frequency.

12. A computer-readable medium carrying one or more sequences of instructions for recovering spectral features using a chirped optical field, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

receiving a detected time series that represents a temporally varying intensity of an optical signal in response to an interaction between a target optical spectrum and a chirped optical field, wherein

the chirped optical field is an optical field that has a monochromatic frequency that varies in time, and

the target optical spectrum is an optical frequency dependent optical property of a material or device;

determining a phase correction factor based only on one or more properties of the chirped optical field; and

correcting the detected time series based on the phase correction factor to produce an output time series that reproduces in time a shape of the target spectrum in frequency.

13. A computer-readable medium as recited in claim 12 , said step of determining the phase correction factor further comprising determining the phase correction factor based on a quadratic phase term.

14. A computer-readable medium as recited in claim 12 , wherein:

the chirped optical field has a plurality of well-known values for a corresponding plurality of well-known properties; and

said step of determining the phase correction factor further comprising determining the phase correction factor based on the well-known values.

15. A computer-readable medium as recited in claim 14 , wherein the plurality of well-known properties include:

a constant chirp rate (κ) that indicates a change in frequency of the chirped optical field with time, and

a start frequency (νs) that indicates an initial frequency at a start of the chirped optical field.

16. A computer-readable medium as recited in claim 15 , said step of determining the phase correction factor further comprising determining a frequency (ν) dependent correction factor based on a chirped phase term φc given by the equation

ti φ c=exp[i π(2 νsν−ν 2 )/κ]

that includes an effect of a quadratic phase, where i is the square root of −1 and π is the well known ratio of a circumference to a diameter.

17. A computer-readable medium as recited in claim 16 , said step of correcting the detected time series based on the phase correction factor further comprising:

determining a Fourier transform of the detected time series;

multiplying the Fourier transform of the detected time series by the correction factor equal to the reciprocal of the phase term φc to produce a corrected transform; and

determining an inverse Fourier transform of the corrected transform to produce the output time series.

18. A computer-readable medium as recited in claim 16 , said step of correcting the detected time series based on the phase correction factor further comprising:

determining an inverse Fourier transform of the correction factor equal to the reciprocal of the phase term φc to produce a transformed correction; and

convolving the transformed correction with the detected time series to produce the output time series.

19. A computer-readable medium as recited in claim 18 , said step of correcting the detected time series based on the phase correction factor further comprising:

determining a Fourier transform of the detected time series;

multiplying the Fourier transform of the detected time series by the correction factor proportional to the reciprocal of the Fourier transform of the chirped optical field to produce a corrected transform; and

determining an inverse Fourier transform of the corrected transform to produce the output time series.

20. A computer-readable medium as recited in claim 12 , said step of determining the phase correction factor further comprising determining a Fourier transform of the chirped optical field.

21. A computer-readable medium carrying one or more sequences of instructions for recovering spectral features using a chirped optical field, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

receiving a detected time series that represents a temporally varying intensity of an optical signal in response to an interaction between an incident optical field having a target optical spectrum and a material with a chirped spectral grating, wherein the chirped spectral grating is a spectral grating of grating period that varies with optical frequency, and

determining a phase correction factor based only on one or more properties of the chirped spectral grating; and

correcting the detected time series based on the phase correction factor to produce an output time series that reproduces in time a shape of the target spectrum in frequency.