Fourier domain low-coherence interferometry for light scattering spectroscopy apparatus and method

Abstract

An apparatus and method for obtaining depth-resolved spectra for the purpose of determining the size of scatterers by measuring their elastic scattering properties. Depth resolution is achieved by using a white light source in a Michelson interferometer and dispersing a mixed signal and reference fields. The measured spectrum is Fourier transformed to obtain an axial spatial cross-correlation between the signal and reference fields with near 1 μm depth-resolution. The spectral dependence of scattering by the sample is determined by windowing the spectrum to measure the scattering amplitude as a function of wavenumber.

1. A method of obtaining depth-resolved spectra of a sample for determining size and depth characteristics of scatterers within the sample, comprising the steps of:
 emitting a beam onto a splitter, wherein the splitter is fixed with respect to the sample, and wherein the splitter splits light from the bean beam to produce a reference beam, which is reflected to produce a reflected reference beam, and an input beam to the sample comprised of a substrate having a first surface and a second surface; 
 cross-correlating the reflected reference beam with a reflected sample beam scattered from the sample as a result of the input beam by mixing the reflected reference beam and the reflected scattered sample beam; 
 spectrally dispersing the mixed reflected reference beam and the reflected scattered sample beam to yield a single spectrally resolved, spectrally-resolved cross-correlated reflection profile having depth-resolved information about the reflected scattered sample beam; and 
 generating a spectroscopic depth-resolved reflection profile, by processing that includes characteristics of scatterers within the sample by:
 providing one or more spectral windows of the single spectrally-resolved cross-correlated reflection profile by: at a plurality of different center wavelengths, applying a window to the single spectrally-resolved cross-correlated reflection profile at, each of the one or more spectral windows having a given center wavelength to obtain spectral information at the given center wavelengthabout the sample for each of the one or more spectral windows; and 
 converting the windowedapplying a Fourier transform to the spectral information via a Fourier transform to recover depth-resolved information about the sample at all each given center wavelengths wavelength simultaneously. 
 
 
     
     
       2. The method of  claim 1 , further comprising recovering size information about the scatterers from the spectroscopic depth-resolved reflection profile. 
     
     
       3. The method of  claim 2 , wherein recovering the size information is obtained by measuring a frequency of a spectral modulation in the spectroscopic depth-resolved reflection profile. 
     
     
       4. The method of  claim 2 , wherein recovering the size information is obtained by comparing the spectroscopic depth-resolved reflection profile to a predicted analytical or numerical scattering distribution of the sample. 
     
     
       5. The method of  claim 1 , wherein applying a processing algorithm providing one or more spectral windows is comprised of applying a providing one or more Gaussian window windows, one or more multiple simultaneous windows, or one or more other window. 
     
     
       6. The method of  claim 1 , wherein the splitter is comprised from the group consisting of a beam splitter and an optical fiber splitter. 
     
     
       7. The method of  claim 1 , wherein emitting a beam onto the splitter comprises emitting a collimated beam. 
     
     
       8. The method of  claim 7 , wherein the input beam comprises a collimated beam. 
     
     
       9. The method of  claim 7 , wherein the reflected reference beam comprises a collimated beam. 
     
     
       10. The method of  claim 1 , wherein the beam is comprised of a light comprised of white light from an arc lamp or thermal source. 
     
     
       11. The method of  claim 1 , wherein cross-correlating the reflected reference beam with the reflected scattered sample beam comprises determining an interference term by measuring the intensity of the reflected scattered sample beam and the reflected reference beam independently and subtracting them from the total intensity of the reflected scattered sample beam. 
     
     
       12. The method of  claim 1 , wherein the reflected reference beam is created by reflecting the reference beam reflected off of a reference mirror. 
     
     
       13. The method of  claim 1 , wherein the length of the path of the reference beam is fixed. 
     
     
       14. The method of  claim 1 , wherein the splitter is attached to a fixed reference arm. 
     
     
       15. The method of  claim 1 , wherein the sample is attached to a fixed sample arm. 
     
     
       16. The method of  claim 1 , wherein dispersing the mixed reflected reference beam and reflected scattered sample beam is performed using a spectrograph. 
     
     
       17. A method of obtaining depth-resolved spectra of a sample comprised of a substrate having a first surface and a second surface for determining size and depth characteristics of scatterers within the sample, comprising the steps of:
 emitting a beam onto a splitter wherein the splitter is fixed with respect to the sample, wherein the splitter splits light from the beam to produce a reference beam, which is reflected to produce a reflected reference beam, and an input beam to the sample comprised of a substrate having a first surface and a second surface; 
 cross-correlating the reflected reference beam with a first reflected scattered sample beam comprised of a first portion of light scattered from the first surface, by mixing the reflected reference beam and the first portion of light; 
 cross-correlating the reflected reference beam with a second reflected scattered sample beam comprised of a second portion of light scattered from the second surface, by mixing the reflected reference beam and the second portion of light; 
 spectrally dispersing the mixed reflected reference beam and the first reflected scattered sample beam to yield a first single first spectrally dispersed, spectrally-resolved cross-correlated reflection profile having depth-resolved information about the first surface of the substrate; 
 spectrally dispersing the mixed reflected reference beam and the second reflected scattered sample beam to yield a second single second spectrally dispersed, spectrally-resolved cross-correlated reflection profile having depth-resolved information about the second surface of the substrate; 
 generating a first spectroscopic depth-resolved reflection profile by processing the single spectrally dispersed, first cross-correlated reflection profile by: that includes characteristics of scatterers within the sample by:
 at a pluralityproviding one or more first spectral windows of different center wavelengths, applying a window to the first single first spectrally dispersed,spectrally-resolved cross-correlated reflection profile, each of the one or more first spectral windows at a given center wavelength to obtain spectral information at the given center wavelength; and 
 converting the windowed spectral information via a Fourier transform to recover depth-resolved first spectral information about the first surface of the substrate at all center wavelengths simultaneously for each of the one or more first spectral windows; and 
 
 applying a Fourier transform to the first spectral information to recover depth information about the first surface at each given center wavelength simultaneously; andgenerating a second spectroscopic depth-resolved reflection profile by processing the singlethat includes characteristics of scatterers within the sample by:
 providing one or more second spectrally dispersed, cross-correlated reflection profile by: at a plurality of different center wavelengths, applying a window to the single spectral windows of the first spectrally dispersed, single spectrally-resolved cross-correlated reflection profile, each of the one or more second spectral windows at a given center wavelength to obtain spectral information at the given center wavelength; and   converting the windowed spectral information via a Fourier transform to recover depth-resolvedsecond spectral information about the second surface of the substrate at all center wavelength simultaneouslyfor each of the one or more second spectral windows; and   applying a Fourier transform to the second spectral information to recover depth information about the second surface at each given center wavelength simultaneously.   
 
     
     
       18. The method of  claim 17 , wherein recovering size information about the sample is comprised of determining a ratio of the first spectroscopic depth-resolved reflection profile and the second spectroscopic depth-resolved reflection profile. 
     
     
       19. The method of  claim 17 , wherein the first surface is the front of the substrate and the second surface is the back of the substrate or a sample attached to or near the back of the substrate. 
     
     
       20. An apparatus for obtaining depth-resolved spectra of a sample in order to determine the size and depth characteristics of scatterers within the sample, comprising:
 a sample that receives a sample beam and reflects a reflected sample beam in response, wherein the reflected sample beam contains light scattered from the sample; 
 a receiver that is fixed with respect adapted to the sample, that receives receive a reflected reference beam and the reflected a scattered sample beam and cross-correlates containing light scattered from a sample in response to the sample receiving a sample beam, wherein the receiver is further adapted to cross-correlate the reflected reference beam with the reflected scattered sample beam; 
 a detector that adapted to spectrally disperses disperse the cross-correlated reflected reference beam and reflected scattered sample beam to yield a single spectrally dispersed, spectrally-resolved cross-correlated reflection profile having depth-resolved information about the reflected scattered sample beam; and 
 a processor unit adapted to: generate a spectroscopic depth-resolved reflection profile, by processing the single spectrally-resolved cross-correlated reflection profile by: at a plurality that includes characteristics of different center wavelengths, applying a window to scatterers within the sample by:
 providing one or more spectral windows of the single spectrally-resolved cross-correlated reflection profile, each of the one or more spectral windows at a given center wavelength to obtain spectral information at the given center wavelength about the sample for each of the one or more spectral windows; and 
 convertingapplying a Fourier transform to the spectral information via Fourier transform to recover depth-resolved spectral depth information about the sample at all each given center wavelengths wavelength simultaneously. 
 
 
     
     
       21. The apparatus of  claim 20 , wherein the processor unit is further adapted to recover size information about the sample from the spectroscopic depth-resolved reflection profile. 
     
     
       22. The apparatus of  claim 20 , wherein the processor unit is further adapted to recover the size information by measuring a frequency of a spectral modulation in the spectroscopic depth-resolved reflection profile. 
     
     
       23. The apparatus of  claim 20 , wherein the processor unit is further adapted to recover the size information by comparing the spectroscopic depth-resolved reflection profile to a predicted analytical or numerical scattering distribution of the sample measuring a frequency of a spectral modulation in the spectroscopic depth-resolved reflection profile. 
     
     
       24. The apparatus of  claim 20 , wherein applying a processing algorithm providing one or more spectral windows is comprised of applying a providing one or more Gaussian window windows, one or more multiple simultaneous windows, or one or more other window. 
     
     
       25. The apparatus of  claim 20 , wherein the receiver is comprised of a splitter. 
     
     
       26. The apparatus of  claim 25 , wherein the splitter is comprised from the group consisting of a beam splitter and an optical fiber splitter. 
     
     
       27. The apparatus of  claim 20 , wherein the sample beam comprises a collimated beam. 
     
     
       28. The apparatus of  claim 20 , wherein the reflected reference beam comprises a collimated beam. 
     
     
       29. The apparatus of  claim 20 , wherein the received beam is comprised of a light comprised from the group consisting of a white light generated by an arc lamp or thermal source. 
     
     
       30. The apparatus of  claim 20 , wherein the length of the path of the reference beam is fixed. 
     
     
       31. The apparatus of  claim 20 , wherein the receiver is attached to a fixed reference arm. 
     
     
       32. The apparatus of  claim 20 , wherein the sample is attached to a fixed sample arm. 
     
     
       33. The apparatus of  claim 20 , wherein the detector is comprised of a dispersive element. 
     
     
       34. The apparatus of  claim 33 , wherein the dispersive element is a spectrograph. 
     
     
       35. An apparatus for obtaining depth-resolved spectra of a sample comprised of a substrate having a first surface and a second surface in order to determine the size and depth characteristics of scatterers within the sample, comprising:
 a sample that receives a sample beam and reflects a first and second reflected sample beam in response, wherein the first reflected sample beam is comprised of a first portion of light scattered from the first surface of the sample, and where the second reflected sample beam is comprised of a second portion of light scattered from the second surface of the sample; 
 a receiver that is fixed with respect to the sample, that receives adapted to receive a reflected reference beam and the , a first scattered sample beam containing light scattered from a first surface in response to the first surface receiving a sample beam, and a second reflected scattered sample beams beam containing light scattered from a second surface in response to the first surface receiving a sample beam, and cross-correlates cross-correlate the reflected reference beam with the first reflected scattered sample beam, and the reflected reference beam with the second reflected scattered sample beam; 
 a detector that adapted to spectrally disperses disperse the cross-correlated reflected reference beam and the first reflected scattered sample beam to yield a first single first spectrally dispersed, spectrally-resolved cross-correlated reflection profile having depth-resolved information about the first surface, and spectrally disperses disperse the cross-correlated reflected reference beam and the second reflected scattered sample beam to yield a second single second spectrally dispersed, spectrally-resolved cross-correlated reflection profile having depth-resolved information about the second surface; and 
 a processor unit adapted to: 
 generate a first spectroscopic depth-resolved reflection profile, by processing the single first cross-correlated reflection profile by, at a plurality of different center wavelengths: that includes characteristics of scatterers within the sample by:
 applying a window to theproviding one or more first spectral windows of the first single firstspectrally-resolved cross-correlated reflection profile, each of the one or more first spectral windows at a given center wavelength to obtain spectral information at the given center wavelength; and 
 converting the spectral information via Fourier transform to recover depth-resolved first spectral information about the first surface of the sample at all center wavelengths simultaneously substrate for each of the one or more first spectral windows; and 
 applying a Fourier transform to the first spectral information to recover depth information about the first surface at each given center wavelength simultaneously; and 
 
 generate a second spectroscopic depth-resolved reflection profile, that includes characteristics of scatterers within the sample as a function wavelength and depth by processing the single: 
 providing one or more second cross-correlated reflection profile by:
 at a plurality of different center wavelengths, applying a window to the single spectral windows of the second single spectrally-resolved cross-correlated reflection profile, each of the one or more second spectral windows at a given center wavelength to obtain second spectral information at the given center wavelength about the second surface of the substrate for each of the one or more second spectral windows; and   converting the spectral information viaapplying a Fourier transform to the second spectral information to recover depth-resolved spectraldepth information about the second surface of the sample at all each given center wavelengths wavelength simultaneously.   
 
     
     
       36. The apparatus of  claim 35 , wherein the processor unit is further adapted to recover size information about the sample by determining a ratio of the first spectroscopic depth-resolved reflection profile and the second spectroscopic depth-resolved reflection profile. 
     
     
       37. The apparatus of  claim 35 , wherein the first surface is the front of the substrate and the second surface is the back of the substrate or a sample attached to or near the back of the substrate. 
     
     
       38. The method of claim 1, comprising:
 providing the one or more spectral windows to the single spectrally-resolved cross-correlated reflection profile as a plurality of spectral windows at a plurality of different center wavelengths to obtain the spectral information for each of the one or more spectral windows; and   applying the Fourier transform to the spectral information to recover the depth-resolved information about the sample at all of the plurality of different center wavelengths simultaneously.   
     
     
       39. The method of claim 17, comprising:
 providing the one or more first spectral windows to the first single spectrally-resolved cross-correlated reflection profile as a plurality of spectral windows at a plurality of different center wavelengths to obtain the first spectral information for each of the plurality of spectral windows; and   applying the Fourier transform to the first spectral information to recover the depth-resolved information about the first surface of the substrate at all of the plurality of different center wavelengths simultaneously.   
     
     
       40. The method of claim 17, comprising:
 providing the one or more second spectral windows to the second single spectrally-resolved cross-correlated reflection profile as a plurality of spectral windows at a plurality of different center wavelengths to obtain the second spectral information for each of the plurality of spectral windows; and   applying the Fourier transform to the second spectral information to recover the depth-resolved information about the second surface of the substrate at all of the plurality of different center wavelengths simultaneously.   
     
     
       41. The method of claim 17, comprising:
 providing the one or more first spectral windows to the first single spectrally-resolved cross-correlated reflection profile as a plurality of first spectral windows at a plurality of different center wavelengths to obtain the first spectral information for each of the plurality of first spectral windows;   providing the one or more second spectral windows to the second single spectrally-resolved cross-correlated profile as a plurality of second spectral windows at the plurality of different center wavelengths to obtain the second spectral information for each of the plurality of second spectral windows;   applying the Fourier transform to the first spectral information to recover the depth-resolved information about the first surface of the substrate at all of the plurality of different center wavelengths simultaneously; and   applying the Fourier transform to the second spectral information to recover the depth-resolved information about the second surface of the substrate at all of the plurality of different center wavelengths simultaneously.   
     
     
       42. The apparatus of claim 20, wherein the processor unit is adapted to:
 provide the one or more spectral windows to the single spectrally-resolved cross-correlated reflection profile as a plurality of spectral windows at a plurality of different center wavelengths to obtain the spectral information for each of the plurality of spectral windows; and   apply the Fourier transform to the spectral information to recover the depth-resolved information about the sample at all of the plurality of different center wavelengths simultaneously.   
     
     
       43. The apparatus of claim 35, wherein the processor unit is adapted to:
 provide the one or more first spectral windows to the first single spectrally-resolved cross-correlated reflection profile as a plurality of spectral windows at a plurality of different center wavelengths to obtain the first spectral information for each of the plurality of spectral windows; and   apply the Fourier transform to the first spectral information to recover the depth-resolved information about the first surface of the substrate at all of the plurality of different center wavelengths simultaneously.   
     
     
       44. The apparatus of claim 35, wherein the processor unit is further adapted to:
 provide the one or more second spectral windows to the second single spectrally-resolved cross-correlated reflection profile as a plurality of spectral windows at a plurality of different center wavelengths to obtain the second spectral information for each of the plurality of spectral windows; and   apply the Fourier transform to the second spectral information to recover the depth-resolved information about the second surface of the substrate at all of the plurality of different center wavelengths simultaneously.   
     
     
       45. The method of claim 2, in which the scatterers are cell nuclei. 
     
     
       46. The method of claim 3, in which the scatterers are cell nuclei. 
     
     
       47. The method of claim 4, in which the scatterers are cell nuclei. 
     
     
       48. The method of claim 21, in which the scatterers are cell nuclei. 
     
     
       49. The method of claim 22, in which the scatterers are cell nuclei. 
     
     
       50. The method of claim 23, in which the scatterers are cell nuclei. 
     
     
       51. The method of claim 1, wherein the bandwidth of at least one of the one or more spectral windows is between approximately 4.4 nm and 21.0 nm. 
     
     
       52. The method of claim 1, wherein the bandwidth of each of the one or more spectral windows is between approximately 4.4 nm and 21.0 nm. 
     
     
       53. The method of claim 17, wherein the bandwidth of at least one of the one or more spectral windows of the first single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       54. The method of claim 17, wherein the bandwidth of at least one of the one or more spectral windows of the second single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       55. The method of claim 48, wherein the bandwidth of at least one of the one or more spectral windows of the first single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       56. The method of claim 17, wherein the bandwidth of each of the one or more spectral windows of the first single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       57. The method of claim 17, wherein the bandwidth of each of the one or more spectral windows of the second single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       58. The apparatus of claim 20, wherein the bandwidth of at least one of the one or more spectral windows is between approximately 4.4 nm and 21.0 nm. 
     
     
       59. The apparatus of claim 20, wherein the bandwidth of each of the one or more spectral windows is between approximately 4.4 nm and 21.0 nm. 
     
     
       60. The apparatus of claim 35, wherein the bandwidth of at least one of the one or more spectral windows of the first single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       61. The apparatus of claim 35, wherein the bandwidth of at least one of the one or more spectral windows of the second single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       62. The apparatus of claim 61, wherein the bandwidth of at least one of the one or more spectral windows of the first single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       63. The apparatus of claim 35, wherein the bandwidth of each of the one or more spectral windows of the first single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm. 
     
     
       64. The apparatus of claim 35, wherein the bandwidth of each of the one or more spectral windows of the second single spectrally-resolved cross-correlated reflection profile is between approximately 4.4 nm and 21.0 nm.