here is great interest in the development of opticalnterference imaging spectrometer with much largerptical throughput1 that can be widely used in theelds of space and temporal information survey, com-unication, and metrologies. Fourier-transform
pectroscopy, based on the two-beam interferencehenomenon, is a powerful spectroscopic technique inhe wavelength ranges of infrared, visible, andltraviolet.2–4 The power spectrum of a Fourierransform of the interferogram corresponds to thepectral distribution of the input light.1 The inter-erence imaging spectrometers based on Michelsonnterferometers are called temporally modulated im-ging interferometers.5–8 However, these instru-ents require high-quality mirror-scanningechanisms, and the temporal resolution is limited
y the maximum mechanical scanning rate. Onean overcome these problems by using an interferom-ter in which the interferogram is produced in thepatial rather than in the temporal domain. This
C. Zhang �[email protected]� is with the School of Science,i’an Jiaotong University, Xi’an 710049, China. B. Zhao and. Xiangli are with the Xi’an Institute of Optics and Precisionechanics, Chinese Academy of Sciences, Xi’an 710068, China.Received 6 February 2004; revised manuscript received 4 June
004; accepted 20 July 2004.0003-6935�04�336090-05$15.00�0
ind of imaging spectrometer is called a spatiallyodulated imaging spectrometer.3,9–12 Most of
hese spectrometers are based on the lateral shearingnterferometer, like the Sagnac, Mach–Zehnder, tri-ngle common path, and birefringent interferom-ters. The advantages of a spatially modulatednterference imaging spectrometer over a temporally
odulated interference imaging spectrometer arehat it has no moving parts is compact and low cost,nd has a high stability against vibrations; it also hashe ability to obtain the interferogram in real time.ince these spectrometers have a slit in the system,hey have a small field of view, which greatly limitsptical throughput. A static polarization imagingpectrometer without a slit was presented by Zhangt al.13–17 in 2000.
In this paper, we present a novel wide field of viewolarization interference imaging spectrometerWPIIS� based on a modified Savart polariscope.his design overcomes the narrow slit limitationsnd with a wider field of view and a higher opticalhroughput. The WPIIS will be a great applicationn the fields of aviation and space flight and the de-ection of a distant target or a faint signal.
o explain clearly the principle of the imaging spec-rometer WPIIS, we need to briefly review a typicalolarization interference imaging spectrometer.
igure 1 shows the optical layout of an angle-shear
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olarization interference imaging spectrometer, dig-tal array scanned interferometer (DASI) using a bi-efringent crystal,18 which belongs to a spatiallyodulated interference imaging spectrometer.The fore-optical system �a telescope� forms a two-
imensional spatial image at its imaging plane.his plane is the object plane for interference imag-
ng optics and the fore-focal plane of a collimator lens.n aperture �or narrow slit� is placed on the plane.n input ray is collimated by a pretelescope system;parallel ray is polarized by a 45° linear polarizer
nd then split into two polarized components by aollaston prism. The Wollaston prism shears the
wo components with a slight angle, and the analyzer45° linear polarizer� is used to make two componentsnterfere. The virtual images of slit are localized inplane that is perpendicular to the plane of the paper
n Wollaston prism.19 An image-forming system in-luding an imaging lens and a cylindrical optic issed, and the detector is placed on their common focallane. When the cylindrical optic is oriented so thatt has power only in the horizontal direction, the ob-ect �target� is imaged on the detector in the horizon-al direction. The interferograms produced by theorresponding points of the two virtual images areecorded with a two-dimensional CCD detector.
It is clear that DASI adopts the Wollaston prism,nd the angle shearing has a narrow slit just likeome of the other spatially modulated imagingpectrometers.3,9–12 Although the width of this slitas nothing to do with spectral resolution, it is re-tricted by spatial resolution in the flying direction.15
wing to the existence of the narrow slit, thehroughput is seriously limited. Accordingly, thesenstruments are not able to detect a distant target or
faint signal.
. WPIIS Setup
. Optics and Designs
igure 2 shows an optical layout of the developedPIIS. The system consists of three lenses, two po-
arizers, a modified Savart polariscope, a two-imensional CCD camera, and an imaging dataandling system. An object located at infinite dis-ance is imaged on the back focal plan of lens 0 andhe front focal plane of lens 1. This image is theetected target of the system. The CCD camera is
ocated on the back focal plane of lens 2. The polar- d
2
zer P1, the modified Savart polariscope, and the an-lyzer P2 are placed between lens 1 and lens 2. Theystem is put on the motor–driver stage �or carried byatellite�, which can move the relative object �orushbroom�. This new mode of data acquisition ishe so-called temporarily spatially mixing modulatedpectrum-obtaining mode.15
The fore-optics system �lenses L0 and L1� collimatehe input rays and then the lenses are polarized by ainear polarizer P1, which consequently is split intowo polarized components by a modified Savart po-ariscope. The modified Savart polariscope shearshe two components laterally. The analyzer P2 issed to ensure that the two components have theame vibrating direction, and the lens L2 reuniteshese two components in its focal plane. The inter-erogram and the target image in the spatial domainre recorded by an area array detector. Since theetector plane is the focal plane of lens L2, this opticss a source-doubling setup. The WPIIS uses the bi-efringence of a modified Savart polariscope to intro-uce a path difference between the orthogonalolarizations. The interference fringe formed on theetector is equivalent to that of equal inclination.he visibility of the interference fringe is therefore
ndependent of the light-source size. The main ad-antages of the practice are that fringes aretraighter and the angles of incidence cannot be re-tricted to small values or a large field of view. Thenique advantages in terms of principle are thathere is no narrow slit in the device, there is a wideeld of view under compensating, and the throughputf the system is raised substantially compared withhe spatially modulated imaging spectrometer. Onhe other hand, a lateral shearing beam splittersompensation Savart polariscope is installed in theormal imaging optics, so the image of the target asell as the interferogram can be obtained at the same
ime, and eventually the spectrum of input light cane reconstructed.
. Modified Savart Polariscope
he key component in the WPIIS is a modified Savartolariscope, which is shown in Fig. 3. It is made upf two identical plates cut at 45° to the optic axes andith their principle sections parallel; the two opticxes are perpendicular to each other. A half-wavelate is inserted between the left plate and the rightlate of the polariscope. In the first plate the inci-
ig. 2. Optical layout of WPIIS based on a modified Savart po-ariscope.
ent ray is sheared in half, the ordinary ray o and the
xtraordinary ray e. Because the half-wave plateauses a 90° rotation of the linear polarization statesor each of the incident rays, the ordinary ray o in therst plate becomes extraordinary ray e in the secondlate, and vice versa. As shown in Fig. 2, the lateralisplacement �the distance between the two virtualources, two rays oe and eo� is twice that given by aimple plate19
d � 2t��n02 � ne
2���n02 � ne
2��. (1)
his formula can be used to determine any corre-ponding points of the two virtual images. The pathifference between the eo and oe rays is given by19
�1 � 2t��a2 � b2���a2 � b2��cos � sin i, (2)
here a 1�ne, b 1�no, and t is the thickness ofhe crystal plate. 2t is the total thickness of theodified Savart polariscope, i is the angle of inci-
ence, and � is the angle between the plane ofncidence and the principle section of the crystallate, usually � 0.
. System Configuration
atural light is used for the light source, the wave-ength is 0.45–0.9 �m, and wave number � is2222.2–11111.1 cm�1:
�� � �max � �min � 11111.1 cm�1,
here the spectrum sector is N 128. Hence for awo-sided sampling interferogram, the resolution ofhe WPIIS is given theoretically by
� � 11111.1 cm�1�128 � 86.8 cm�1. (3)
To satisfy the resolution, parameters of the systemre selected: an area detector �512 � 512 pixels� andn image grabber are used as the signal samplingystem. The size of each pixel is 12 � 12 �m2. Theaximum optical path difference between the two
where xmax is a half of the detector size, whichubtends an angle � xmax�f2 at the center of L2.he focal length f2 of collimator mirror L2 can then bealculated from Eqs. �4�–�6�; we get
f2 � dxmax��max � 1.333 � 3.072�0.0576
� 71.1 mm. (7)
The Savart polariscope is made of two 30 � 30 � 6m3 calcite crystal plates. The distance between
he two virtual sources split by the Savart polariscopes d 1.333 mm �n0 � 1.66527, ne � 1.48956; Ab-orptivity, �o �e 0�. The focal length of Lo and1 are fo f1 50 mm, respectively.
. Wide-Field-of-View Compensation Principle
n a polarizing imaging spectrometer, the Savart po-ariscope’s path difference between the two virtualources is given by15,19
� � ta2 � b2
a2 � b2 �cos � � sin ��
�a2 � b2
�a2 � b2�3�2
a2
�2�cos2 � � sin2 ��sin2 i
� terms in sin4 i . . . , (8)
where i is the angle of incidence and � is the angleetween the plane of incidence and the principal sec-ion of the crystal plate. Since the term in sin2 i doesot vanish, the fringes will be straight only in theenter of the field.
Because the fringes produced by a Savart polari-cope are not perfectly straight, even for small anglesf incidence, for the applications of the imaging spec-rometer the fringes are required to be more nearlytraight, and angles of incidence cannot be restrictedo small values. To overcome the bent fringes ofar-field and spectrum aberrance, we use a modifiedavart polariscope. Since there is a half-wave plateetween the two constituent plates the path differ-nce due to the second plate is to be subtracted fromhat due to the first; thus the net path differenceetween the eo ray and the oe ray is given by19
� � 2ta2 � b2
a2 � b2 cos � sin i. (9)
There is no term in i2; the i3 term is almost alwaysegligible. Because the expression for the path dif-erence does not contain terms of the second andigher powers of sin i, under larger angles of inci-ence the fringes are equidistant straight lines thatre perpendicular to the principal section of thelates. The fringes are straight over a much largereld than in the case of a simple Savart polariscope.
. Throughput Comparison with DASI and Spatiallyodulated Interferometer Imaging Spectrometer
s we know, the optical throughput of an interferenceype’s imaging spectrometer is at least 190 times
reater than that of a dispersive imaging spectrom-
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ter.1 DASI and a spatially modulated interferencemaging spectrometer each belong to this type of thenterference. Because each has narrow slit, al-hough the width of the slit has nothing to do withpectral resolution, it is restricted by spatial resolu-ion in the flying direction, and the throughput of theystem is largely limited. The narrow slit is re-laced by the field-of-view stop in the WPIIS, thus thehroughput is N�2 times as big as DASI and thepatially modulated interference imaging spectrom-ter �N is the ratio of the width of the field-of-viewtop against the width of narrow slit�. Because N issually taken to be 1–2 orders of magnitude, thehroughput of WPIIS is 1–2 orders of magnitudearger than that of DASI and the spatially modulatednterference imaging spectrometer.15
. Experimental Results
e performed several imaging spectroscopy experi-ents by using the WPIIS. Figures 4 and 5 are a
olychromatic light source’s and a monochromaticight source’s interferogram and target’s image, re-pectively, with a large angle of incidence.Figures 4 and 5 are two examples of an individual
nterferogram of different objects. Each is sampledt one time in their own process of the final interfero-ram’s formation of a specific spatial location. Al-hough the instantaneous interferogram for a singlerame is obtained at one time, the complete interfero-
ig. 4. Polychromatic light source’s interferogram and the tar-et’s image with a large angle of incidence.
ig. 5. Monochromatic light source’s interferogram and the tar-
et’s image with a large angle of incidence.
2
ram for a specific spatial location within the imageequires multiple frames over time as well as thepatial synchronization of locations �pixels� betweenrames. Each of the frames has been sampled at aifferent time and position than the others, so theame spatial location has a different position in eachrame. The final interferogram of a specific spatialocation, whose spectrum can be obtained with fastourier transform, requires the arrangement, assem-ling, and synchronization of corresponding pixels ofultiple frames.Figure 6 is the original interferogram of monochro-atic light � 488.8 nm� under a field of view of10°. Figure 7 is obtained with the apodization bytriangle function for Fig. 6. Figure 8 shows the
ourier transform of the interferogram presented inig. 7, i.e., the reconstructed spectrum of the mono-hromatic light obtained through fast Fourier trans-
ig. 6. Monochromatic light source’s original interferogram un-er field of view angle of �10°.
ig. 7. Interferogram with the apodization by a triangle function.
Fig. 8. Reconstructed spectrum of monochromatic light.
orm with the apodization by a triangle function andphase correction.
. Conclusion
he WPIIS is a type of time–space mixing modulatedcheme; the optical path difference modulated by usef a change of the field of view. The interferogramould not obtained at the same time but was obtainedhrough observation of the change of the optical pathifference during the period that the ray comes fromhe point of target going through the field of view withhe push brooming �scanning� of a satellite.
Because the WPIIS has no narrow slit or movingarts, the optical path difference has not changeduch with field of view, or the change is very little, so
he field of view angle can reach �10°–15°, and is 4–5imes as large as a common interference imagingpectrometer. When the two beams travel along al-ost the same path, it has advantages of stability, aider field of view, and high throughput and is able toe made compact. Additionally, because the inter-erogram is produced by the polarized rays, the short-oming is that the detector has a different respondingate against different forms of polarized ray.
The authors gratefully acknowledge the support ofhinese Natural Science Foundation. This researchas supported by the Chinese Natural Science Foun-ation under Contracts 40375010 and 60278019 andy the Science and Technology Plan Foundation ofhaanxi Province under contract 2001K06-G12. Were thankful to Mingjun Zhao for his help with thisaper.
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