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Description  |
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BACKGROUND OF THE INVENTION
This invention relates to Fourier transform spectrometers and specifically
to a new optical interferometer mechanism for use therein.
The Fourier transform spectrometer has become a useful tool for scientific
remote sensing of earth and planetary atmospheres. Use of the Fourier
transform spectrometer for these purposes is described in "Fourier
Spectroscopy in Planetary Research," an article written by R. A. Hanell
and V. G. Kunde in Space Science Review, Vol. 18, pp. 201-256, 1975.
However, Fourier transform spectrometers are very complex precision
electro-optical-mechanical instruments. They require a mechanical slide
mechanism that will move with optical interferometer stability. This
requirement for stability has resulted in systems that are very large and
heavy. Even so, they are still sensitive to tilt misalignments. The
problems encountered in designing a stepping interferometer for Fourier
spectrometers are set out in Spectrometric Techniques, Vol. II, Chapter 2,
"First-Order Optical Design for Fourier Spectrometers," J. B. Breckinridge
and R. A. Schindler, edited by G. A. Vanesse, Academic Press, 1981.
As a result of its complexity and sensitivity, Fourier spectrometers have
been used sparingly in spaceflight applications where precision
spectro-radiometric measurements are required. Attempts have been made to
reduce the instrument's sensitivity to acceleration and the sampling
errors introduced as a result of the nonuniformity of the mechanical
scanning system. See U.S. Pat. No. 4,132,940, issued to Rudolf A.
Schindler on Jan. 2, 1979. However, the problems inherent in a mechanical
stepping scheme have not been solved.
Accordingly, the present invention contemplates an entirely new
configuration for an interferometer which avoids most of the difficulties
inherent in prior art mechanical scanning interferometers. The present
invention results in an entirely new generation of efficient, lightweight,
stable infrared remote radiometer measurement systems.
SUMMARY OF THE INVENTION
The present invention provides higher quality data and exhibits improved
alignment stability over prior art Fourier transform spectrometers. It
functions in an acceleration environment, i.e., spacecraft. It is simpler
in operation, lighter and more rugged than prior Fourier transform
spectrometers. These improvements are the result of a monolithic
interferometer assembly having retro-reflecting mirrors that are not at a
90 degree angle to the propagation vector of the radiation. This tilt
effectively provides the path differences in the two arms of the
interferometer. The resulting interference fringes are detected by a CCD
array wherein the position of each element of the array is an indication
of path length. This invention eliminates physical movement to obtain the
propagation path difference needed to create the varying fringe patterns
in prior art devices.
BRIEF DESCRIPTION OF THE DRAWINGS
The exact nature of this invention as well as other advantages thereof will
be readily apparent from consideration of the following specification
related to the annexed drawings in which like reference numerals designate
like parts throughout the figures thereof, and wherein:
FIG. 1 is a perspective and block diagram illustration of an interferometer
mechanism of the present invention;
FIG. 2 is a graphic illustration of the wavefront interaction occurring in
the interferometer mechanism of the present invention; and
FIG. 3 is an idealized illustration of the interaction between the two
wavefronts to create an interference wavefront and the sampling thereof.
DESCRIPTION OF THE PREFERRED EMBODIMENT
FIG. 1 diagramatically illustrates a Fourier transform spectrometer which
is utilizing an interferometer mechanism 11 built according to the present
invention. The interferometer mechanism 11 is shown in perspective while
the electronics of the spectrometer is shown in block diagram form.
The interferometer mechanism, according to the present invention, utilizes
integrated optics whereby the entrance lens 19, beamsplitter 17, and the
two mirror reflecting surfaces 16 and 18 are all formed as one block of
optical material. The technique by which the mechanism 11 may be
manufactured is described in an article entitled "Two-Dimensional White
Light Coherence Interferometer38 by James B. Breckinridge, Applied
Optics, Vol. 13, p. 2760, November 1974, and an article entitled "A
White-Light Amplitude Interferometer with 180-Degree Rotational Sheer" by
James B. Breckinridge, Optical Engineering, Vol. 17, No. 2, March 1978.
The lens 19 of the interferometer is coated with an opaque aluminum film,
by standard deposition techniques, to form an entrance slot 21 from top to
bottom of the integrated optic cube 15. The lens 19 is curved so that it
functions as a power element or field lens for the interferometer. The
field lens 19 relays the system pupil onto the retro-reflecting mirrors of
the interferometer 11 through a beamsplitter 17 that is actually a part of
the optic cube 15. Radiation 27 enters the system through slot 21. Some of
that radiation 29 passes through the beamsplitter 17 to retro-reflecting
mirror 18. The radiation reflected by beamsplitter 17 to retro-reflecting
mirror 16 is not shown in FIG. 1.
Both radiation beams are reflected back to the beamsplitter 17,
interference recombined as indicated by beam vector 31 into a
two-dimensional wavefront 33. This fringe field is sensed by a
two-dimensional array detector 23 which, for example, could be made up of
a matrix of charge coupled devices 25.
Image sensors utilizing charged-coupled devices are well known in the art.
For example, CCD211 is a 244.times.190 element image sensor manufactured
by Fairchild Semiconductor. A silicon imaging device which comprises a
512.times.320 pixel image sensor is made by RCA.
As is well known, the Fourier transform of the sensed source irradiance
distribution is the spectral irradiance distribution of that source. The
processing technique is standard in the art and is described in
Spectrometric Techniques, Vol. 1, edited by George A. Vanasse, Academic
Press, 1977. Accordingly, the position and intensity sample generated by
the CCD array image sensor 23 is determined by circuitry 35 which then
provides it to a storage facility 37, such as a memory. The storage
facility, when called upon to do so, provides it to equipment that
performs the Fourier processing 39. The result is the spectral
distribution of the source irradiance that can be displayed on an
appropriate device 41, i.e., printer or CRT.
The system, according to the present invention requires no moving parts. It
does not utilize a mechanism to physically step one of the
retro-reflecting mirrors 16 or 18. The only prior art system for an
interferometer which involves no mechanically moving parts of which
applicant is aware, is disclosed in Spectrometric Techniques, Vol. I,
edited by George A. Vanasse, Academic Press, 1977, p. 91. This device
encases a cubic beamsplitter and the two retroreflecting mirrors in a
controlled gas environment. The interferometer is stepped by slowly
filling the space between the beamsplitter and the two mirrors with gases
of different indices of refraction at the same pressure. In contrast to
this prior art device, the preferred embodiment of the present
interferometer cube 15 is solid and uncomplicated. It does not require an
intricate gas control system for varying the gas pressure of two different
gases between the beamsplitter and the two mirrors.
How the path difference is obtained according to the present invention will
be described with reference to FIG. 2. FIG. 2 is a schematic illustration
of the reflection path length between beam 24 that is transmitted through
the beamsplitter 17 and beam 45 that is reflected by the beamsplitter 17.
At least one of the retro-reflecting mirrors, in this case
retro-reflecting mirror 18, is placed at a small angle 49 to the normal of
beam 29. Retro-reflecting mirror 18 is placed so that the path length CB
of beam 29 at the center is equal to the path length CA of beam 45 at the
center. The distances from the center of the beam-splitter 17, at C, to
other points on the mirror surface 18 is either less than, or greater than
the distance from C to mirror surface 16. This is the configuration for
the interferogram shown in FIG. 3, as an example. This equal path position
may be placed anywhere within the field of view of the interferogram to
satisfy any particular requirement.
The two wavefronts generated by the retro-reflecting mirrors 16 and 18 are
shown as wavefront 51 which is reflected from retro-reflecting mirror 16,
and wavefront 58 which is reflected from retro-reflecting mirror 18.
Wavefront 58 is tilted, by a small angle, .alpha. with respect to
wavefront 51. This angle is twice the angle 49 of retro-reflecting mirror
18. The interference combination of wavefront 51 and 58 results in the
interference wavefront 33. This interference is sensed by the image sensor
23 which has a plurality of CCD elements 25 arranged in columns and rows.
The tilt-angle 49 for retro-reflecting mirror 18 is small and works in
combination with the optical filter 13 which is a low-frequency pass (long
wavelength pass) filter in order to create the nonoverlapping interference
fringes or wavefront 33 at the output 31 of the interferometer.
The path lengths in each arm of the interferometer CB and CA are adjusted
to be equal so that the white-light interference fringe is at the center.
The technique for aligning the two retro-reflecting surfaces so that the
white-light interference fringe is at the center is described in "The
Spatial Structure Analyzer and Its Astronomical Applications" by James B.
Breckinridge, a Ph.D. dissertation, published in 1976 and obtainable from
University Microfilms International, 300 North Zeeb Road, Ann Arbor,
Michigan 48106; and in "A Two-Dimensional White-Light Amplitude
Interferometer" by James B. Breckinridge a paper presented at the
International Astronomical Union Colloquium No. 50, Proceedings: High
Resolution Stellar Interferometry, University of Maryland, pp. 31-1 to
31-13, September 1978.
An analysis of the sampling of the interference fringe 33 by a discrete
element array 25 will now be provided with reference to FIG. 3.
The integrated optics interferometer mechanism of the Fourier transform
spectrometer according to the present invention creates the fringe field
33 by interfering two plane waves 51 and 58. These two waves, labeled
AA.sup.1 and BB.sup.1, interfere with angle .alpha., between their
normals, to form a fringe pattern 33 across a detector which has a linear
array of detector elements of width "a", separated by a center-to-center
separation of "b", and covering a linear expanse given by "Nb", where N is
the number of detector elements. Pulse train 61 of FIG. 3 indicates column
sampling of the linear array 23.
Two configurations of wavefront interaction will be analyzed. The first is
with the white-light fringe 62 centered as shown, in FIG. 3. The other is
with the white-light fringe off center.
In FIG. 3 we see that the optical path difference (OPD) (in units of
length) shown by z is a function of y, a distance along the detector
array. If the length of the detector is Nb then the OPD as a function of y
is given by
OPD=.alpha.y
and the OPD for a particular detector element j numbered left to right in
FIG. 3 is
##EQU1##
Recall that j runs from O to N. In linear systems parlance, the array
detector is represented by
##EQU2##
where S (y) is the distribution of sensor area.
In order to sample the spectrum without aliasing, it is necessary to have
two detector elements for each fringe cycle of the shortest wavelength
(highest frequency) light on the focal plane.
We will first consider sampling at this Nyquist spatial frequency (two
detector elements for each fringe cycle). Also, we first consider each
detector element to be infinitely narrow, proceed with the analysis, and
then correct the answer by multiplying the spectrum (Fourier transform of
the interferogram) by the Fourier transform of the detector element of
finite width. The sensor is then,
##EQU3##
Let the source radiation be centered at .lambda..sub.o and extend from a
short wavelength end of .lambda..sub.1 to a long wavelength end of
.lambda..sub.2.
From FIG. 3, we see that the spacing of the fringes of wavelength
.lambda..sub.1 across the sensor plane, for a wavefront tilt of .lambda.
with light of wavelength .lambda..sub.1 is:
.DELTA.y=.lambda..sub.1 /(2.alpha.) (Equation 4)
In the notation used in FIG. 3, then
b=.lambda..sub.1 /(2.alpha.) (Equation 5)
The detector modeled as an array of delta functions is
##EQU4##
with b=.lambda..sub.1 /(2.alpha.). The signal recorded R(y) is the
interferogram I(y), times the sensor function S(y), or
R(y)=I(y).multidot.S(y) (Equation 7)
Recognizing that I(y) is the Fourier transform of I(.sigma.) [intensity as
a function of wavenumber], we can write
R(.sigma.)=I(.sigma.).sym.S(.sigma.) (Equation 8)
and if S(y) is sampled at the Nyquist frequency.
R(.sigma.)=I(.sigma.) (Equation 9)
The finite width of the detector element, given by a in the function Rect
(y/a) in Equation 2, will appear in Equation 9 as a multiplicative factor.
In other words, the Fourier transform of Rect (y/a) which is a sine
function will apodize the spectrum with a multiplicative factor. This
apodization factor is a measurable and stable part of the instrument and
therefore a calibration can be made and the instrumental profile
corrected.
As a practical example, let's consider a 128 element array with 100 micron
pixels separated by 150 microns. The array length is then 19.2 millimeters
long. In FIG. 3, let the OPD be 2 millimeters or 2.0 cm. The spectral
resolution is then 5 cm.sup.-1. If the white-light fringe is centered on
the fringe field which is projected onto the detector array, then we have
64 detectors on each side of the white-light fringe and from
##EQU5##
where n=the number of detector elements or 2n=32 and the resolution
d.sigma.=5 cm.sup.-1, the shortest wavenumber is
.sigma.=(2n) d.sigma. or .sigma.=160 cm.sup.-1.
This is very long infrared, and represents the shortest wavenumber that can
be sampled without aliasing, and without using a filter over the input.
As another practical example, move the white-light fringe to one end of the
interferometer fringe field, and use a detector with 2048 elements, each
detector element of sensitive length 30 microns with a 20 micron gap to
give a spacing of 50 microns. The detector length is then 10.2 cm. A
reasonable angle, .alpha., is 0.05 radians. The optical path difference or
retardation of the interferometer is then (0.05) (10.2)=0.51 cm. From the
equation d.sigma.=1/OPD, d.sigma.=2 cm.sup.-1 and the spectral resolution
is 2 cm.sup.-1 which is uniform over the entire spectral region.
The longest wavenumber or shortest wavelength that one can observe without
aliasing is given by that wavelength which appears across the detector to
give a fringe pattern of such a spacing that two detector elements must
cover one fringe cycle. All wavelengths longer than this will have their
fringe cycles sampled by at least two detector elements and therefore the
spectral information will not be lost or confused through aliasing in the
spectrum. Aliasing is not a serious limitation since bandpass filters will
control effect and these filters are well developed for this region of the
spectrum.
With an angle of 0.05 radians, the cutoff, or shortest wavelength that one
can observe without aliasing, .lambda..sub.c, is given by .lambda..sub.c
=(.DELTA.y).(2)(.alpha.)(50)(2)(0.05)=5 microns or 2,000 cm.sup.-1.
Note that if the prisms are made from transparent materials whose index of
refraction varies as a function of refractive index, then because of the
optical path difference changes across the detector (required to create
the interferogram fringes), there is an optical phase term which varies
from detector element to detector element. This phase term is zero at the
white-light fringe. This phase factor is a measurable and stable part of
the instrument and therefore a calibration can be made and the
instrumental profile corrected.
In order to perform imaging with this interferometer, the entire instrument
is scanned, push-broom style, by mounting it on a moving platform, such as
a spacecraft, to scan the horizon. The slot 21 then causes the different
interferograms to be displayed over adjacent columns of pixels at the
array detector 23. In other words, the scanned image Fourier transform
spectrometer according to the present invention operates much like an
imaging radar.
From the foregoing, it can be seen that a new imaging Fourier transform
spectrometer has been invented which is electronically scanned by parallel
readout of the detector elements rather than using the traditional
scanning techniques such as described in Spectrometric Techniques.
Systems have been devised which provide mirror surfaces at non-normal
angles to the beamsplitter. See Spectrometric Techniques, Vol. I, pp. 80,
81. However, this is the first integrated optics electronically scanned,
imaging Fourier transform spectrometer in the art.
It should be understood, of course, that the foregoing disclosure relates
only to the preferred embodiment of the invention and that numerous
modifications may be made therein without departing from the spirit and
scope of the invention as set forth in the appended claims.
* * * * *
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