CN107741273A - A kind of wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array - Google Patents

A kind of wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array Download PDF

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CN107741273A
CN107741273A CN201710950063.7A CN201710950063A CN107741273A CN 107741273 A CN107741273 A CN 107741273A CN 201710950063 A CN201710950063 A CN 201710950063A CN 107741273 A CN107741273 A CN 107741273A
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long wave
msub
wave infrared
slit
detector array
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CN107741273B (en
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刘银年
赵航斌
张营
丁学专
柴孟阳
孙德新
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Shanghai Institute of Technical Physics of CAS
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01JMEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/28Investigating the spectrum
    • G01J3/2823Imaging spectrometer
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02ATECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A40/00Adaptation technologies in agriculture, forestry, livestock or agroalimentary production
    • Y02A40/10Adaptation technologies in agriculture, forestry, livestock or agroalimentary production in agriculture

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  • Spectroscopy & Molecular Physics (AREA)
  • General Physics & Mathematics (AREA)
  • Spectrometry And Color Measurement (AREA)
  • Transforming Light Signals Into Electric Signals (AREA)

Abstract

The invention discloses a kind of wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array, moved up and down and scanned along vertical slits direction by slit, compensated pendulum mirror synchronizes rotation sweep, the image planes of the different spectral wavelengths of same target are made sequentially to be moved up and down by wavelength size in position of focal plane, so that detector array timesharing obtains the information of all wavelengths spectrum channel.The system realizes the wide cut imaging technique of LONG WAVE INFRARED EO-1 hyperion by alignment infrared detector, its breadth is set not limited by planar array detector scale, and dexterously utilize the synergy of slit and scanning pendulum len, solve with tens wave bands in the whole long wave infrared region on detector array acquisition light spectrum image-forming face, the problem of obtaining target more features information, realize LONG WAVE INFRARED wide range wide cut imaging technique, it is and simple in construction, it is in light weight, low in energy consumption, it can be applied in ground, the airborne or spaceborne wide range Hyperspectral imager of wide cut over the ground.

Description

A kind of wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array
Technical field
The present invention relates to optical element, system, more particularly to hyperspectral imager.Specifically refer to one kind and be used for airborne or star Carry wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array and its imaging side observed over the ground in imager Method.
Background technology
High light spectrum image-forming technology is the remote sensing technology to grow up the eighties, unlike traditional spectrometer, bloom Spectral imaging technology is to integrate imaging and spectrum (collection of illustrative plates), with nanoscale high spectral resolution, is obtaining target two dimension While spatial image information, the synchronous continuous fine spectral information for obtaining target, the detectivity of space remote sensing is set greatly to carry It is high.And compared to visible, near-infrared, short-wave infrared, LONG WAVE INFRARED high light spectrum image-forming technology has unique advantage, spectrum covering Scope has reached nearly ten thousand nanometers, can obtain the fine spectral information of heat radiation of target itself, can not only efficiently identify ground The composition of thing, the construction feature of atural object can also be effectively distinguished, obtains the parameter informations such as temperature and the emissivity of atural object, can be wide It is general to be applied in the observation such as land, air, ocean.
Develop as target acquisition mission requirements court becomes more meticulous with practical direction, the imaging breadth and spectral coverage of remote sensing instrument Width, is related to the efficiency of remote sensing operation and the speed of revisiting period, and obtain target signature information number, wide cut wide range Technology is the important need of high light spectrum image-forming technology businessization development.
Traditional high light spectrum image-forming technology is mainly push-broom type, more to obtain the space dimension of target letter using planar array detector Breath and spectrum dimension information, its principle are:Ground return or radiation signal are assembled through preposition telescope to be imaged on slit jaw, incident Slit makes a picture for wearing rail direction ground strips by and blocking remainder.Pass through the radiation of slit (field stop) Energy passes through beam splitting system, according to spectral dispersion and is imaged in vertical slits length direction on the photosurface of planar array detector. The horizontal direction parallel of photosurface is in a light on slit, as space dimension, each quick bin of water-filling zero diopter being ground strips Compose the picture of passage;The vertical direction of photosurface is dispersion direction, is designated as spectrum dimension, each photosensitive bin of row is atural object band one The picture of spatial sampling visual field (pixel) spectral dispersion.
Therefore, in the prior art, LONG WAVE INFRARED hyperspectral imager is also typically obtained using face battle array Long Wave Infrared Probe Win the confidence breath.And LONG WAVE INFRARED planar array detector is limited by levels such as material, techniques, its array scale is limited.Such as U.S.'s AHI long waves Infrared spectrometer, wavelength band are 7.5 μm~11.5 μm, and wave band number is 256, and the detector used is 256 × 256 yuan HgCdTe detectors (Lucey, P.G., et al., AHI:An airborne long wave infrared hyperspectral imager.Proceedings SPIE Conference on Airborne Reconnaissance, 1998:P36-43).Face array length ripple infrared focal plane detector, particularly long wave infrared region at present, stock size is little, under Face lists several then LONG WAVE INFRARED focal plane device development progress in recent years:
(1) French Sofradir companies report cutoff wavelength for 2005 as 12.1 μm, and scale is 320 × 256 detection Device;
(2) the Raytheon companies in the U.S. report cutoff wavelength for 2005 as 17 μm, and scale is 160 × 160 detection Device;
(3) German AIM companies have developed cutoff wavelength for 2007 as 12.8 μm, and scale is 256 × 256 detector;
(4) it is 9 μm that NASA jet propulsion laboratory (JPL), which have developed cutoff wavelength for 2010, scale 640 × 512 detector;
(5) French Sofradir companies have developed cutoff wavelength for 2013 as 9.3 μm, and scale is 640 × 512 detection Device;
(6) Chinese Academy of Sciences Shanghai Institute of Technical Physics have developed cutoff wavelength for 2015 as 12.5 μm, and scale is 320 × 256 detector;
(7) German AIM companies have developed cutoff wavelength for 2016 as 9 μm, and scale is 1280 × 1024 detector.
As can be seen here, Long Wave Infrared Probe is currently less than 1500 pixels by face battle array size, and with the increasing of face battle array size Add, the cutoff wavelength of detector reduces, and response spectrum wavelength band is small, therefore type LONG WAVE INFRARED high light spectrum image-forming is swept in traditional pushing away Instrument can not realize wide cut wide range.And 10.0~12.5 μm, it is the most important widest application band of LONG WAVE INFRARED.As pixel is empty Between the raising of resolution ratio and the expansion of breadth, the scale demand of pixel module is substantially improved.How cutoff wavelength is solved to 12.5 μ M space dimension pixels scale is more than 2000 yuan, breaks through the limitation of infrared detector technology, realizes LONG WAVE INFRARED wide cut wide range EO-1 hyperion Imaging, it is a current domestic and international big technical barrier urgently to be resolved hurrily.
The content of the invention
The present invention proposes a kind of wide cut LONG WAVE INFRARED hyperspectral imager based on detector array.The purpose of the present invention It is to solve the problems, such as that tradition pushes away to sweep type LONG WAVE INFRARED hyperspectral imager and can not realize that wide cut wide range is imaged, breaks through traditional bloom Technical method of the imager based on planar array detector is composed, and is cleverly scanned using the up and down motion of slit, compensated pendulum mirror is carried out Synchronous rotary compensates, and the image planes of the different spectral wavelengths of same target is sequentially moved up and down by wavelength size in position of focal plane, So that detector array timesharing obtains the information of all wavelengths spectrum channel.The pixel number of in general detector array will compare Planar array detector is higher by 10 times, and the residence time of the pixel of LONG WAVE INFRARED imaging is a few tens of milliseconds, and the time of integration of pixel is only Tradition imaging breadth can be several times as much as so as to be able to acquisition, port number reaches more than tens long waves effectively using hundreds of microseconds are arrived Infrared high spectrum image, realize the LONG WAVE INFRARED high light spectrum image-forming breadth order of magnitude lifted, significantly promote LONG WAVE INFRARED EO-1 hyperion into The operational use of picture.
Therefore, the present invention uses following technical scheme:
A kind of wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array, as shown in figure 1, including looking in the distance Object lens 1, compensated pendulum mirror 2, imaging lens 3, slit 4, LONG WAVE INFRARED beam splitting system 5, LONG WAVE INFRARED spectrum focal plane 6, detector array 7, it is characterised in that:Light from target is after the convergence of telescope 1, and after being reflected by compensated pendulum mirror 2, imaged mirror 3 is imaged On slit 4, by the emittance after slit 4 after LONG WAVE INFRARED beam splitting system 5, on LONG WAVE INFRARED spectrum focal plane 6 Light spectrum image-forming, detector array 7 is recycled to obtain spectrum face information;Slit 4 moves up and down along vertical slits direction and scanned, compensated pendulum Mirror 2 synchronizes rotation sweep, make same target different spectral wavelengths image planes in the position of focal plane 6 by suitable above and below wavelength size Sequence moves, so that the timesharing of detector array 7 obtains the information of all wavelengths spectrum channel.
The invention provides a kind of imaging of the wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array Method, as shown in Figure 1 and Figure 2, by the LONG WAVE INFRARED Hyperspectral imager be mounted on motion platform 8 to target carry out into Picture, specific imaging method is as follows,
Slit 4 is along vertical slits direction from primary optical axis 1-1 is deviateed apart from-LnmaxPosition divide N step step-scan to deviation Primary optical axis 1-1 distances+LnmaxPosition, compensated pendulum mirror 2 is synchronous from deviateing pendulum main shaft 1-2 angle-α nmaxPosition divide N to enter step by step Rotation sweep to deviate main shaft 1-2 angle+α nmaxPosition, the image planes of the different spectral wavelengths of same target are in the position of focal plane 6 Divide N steps order mobile from the bottom up by wavelength size, obtain N number of continuous spectrum segment information, detector array 7 reads its opto-electronic conversion Signal, so that the timesharing of detector array 7 obtains the information of N number of spectrum channel in the whole LONG WAVE INFRARED wave-length coverage of target, institute State the spectral coverage number that N is the LONG WAVE INFRARED Hyperspectral imager;
After detector array 7 obtains the high spectrum image of the whole N number of passage of LONG WAVE INFRARED scope of target, slit 4;Alignment is visited After surveying whole characteristic informations that device 7 is obtained on the LONG WAVE INFRARED spectrum focal plane 6 of the target, slit 4 is quickly from deviation primary optical axis 1-1 Distance+LnmaxPosition return to and deviate primary optical axis 1-1 distance-LnmaxPosition, corresponding compensated pendulum mirror 2 quickly from deviate pendulum master Axle 1-2 angle+α nmaxPosition return to and deviate main shaft 1-2 angle-α nmaxPosition, start to be imaged next target; Repeat the above steps obtain needed for target imaging all wavelengths spectrum channel information;
Wherein, slit 4, which moves up and down, deviates the distance L of primary optical axis 1-1 positionsnDeviate with the rotation sweep of compensated pendulum mirror 2 and put Main shaft 1-2 angle [alpha]nRemain following relational expression:
Wherein, vLFor the movement velocity of slit 4, v is the overall operation speed of motion platform 8, and h is the operation height of motion platform 8; D1For the distance of telephotolens 1 and compensated pendulum mirror 2;D2For compensated pendulum mirror 2 and slot distances.
Wherein, the slit 4, which moves up and down, deviates the ultimate range scope ± Ln of primary optical axis 1-1 positionsmax,
Wherein, H1For the height of LONG WAVE INFRARED spectrum focal plane 6, β is the vertical axle enlargement ratio of LONG WAVE INFRARED beam splitting system 5,
Wherein, H2For the height of slit 4, H3For the height of detector array 7.
The present invention uses above technical scheme, has following advantage:
1) method that traditional hyperspectral imager must use planar array detector is breached so that LONG WAVE INFRARED EO-1 hyperion The breadth of imager is not limited by LONG WAVE INFRARED planar array detector small scale, realize the wide cut of LONG WAVE INFRARED high light spectrum image-forming into As technology, imaging breadth is set to have reached the lifting of the order of magnitude.
2) using the synergy of slit and scanning pendulum len, solve with several on detector array acquisition light spectrum image-forming face Ten wave bands, obtain target more features information the problem of, realize the wide range imaging technique of LONG WAVE INFRARED high light spectrum image-forming, it is more Individual spectral coverage is imaged in the photosensitive member of same detector array, has good uniformity and benchmark.
3) planar array detector being replaced using detector array, whole apparatus structure is simple, in light weight, small volume, low in energy consumption, It can be applied in ground, the airborne or spaceborne wide range Hyperspectral imager of wide cut over the ground.
Brief description of the drawings
Fig. 1 is the structural representation of the wide cut wide range LONG WAVE INFRARED Hyperspectral imager of the invention based on detector array Figure;
Fig. 2 is that the imaging method of the wide cut wide range LONG WAVE INFRARED Hyperspectral imager of the invention based on detector array shows It is intended to;
Fig. 3 is that the narrow slit structure of the wide cut wide range LONG WAVE INFRARED Hyperspectral imager of the invention based on detector array shows It is intended to;
Fig. 4 is the LONG WAVE INFRARED light of the wide cut wide range LONG WAVE INFRARED Hyperspectral imager of the invention based on detector array Compose focal plane structural representation;
Fig. 5 is the detector array of the wide cut wide range LONG WAVE INFRARED Hyperspectral imager of the invention based on detector array Structural representation;
Fig. 6 is that the airborne LONG WAVE INFRARED hyperspectral imager of the embodiment of the present invention carries the signal that aircraft is imaged to target Figure;
Fig. 7 is that the airborne LONG WAVE INFRARED hyperspectral imager carrying aircraft of the embodiment of the present invention carries out imaging acquisition spectrum to target Segment information schematic diagram.
Embodiment
In order that objects, features and advantages of the present invention are more clear, below in conjunction with drawings and Examples, to the present invention A kind of embodiment make more detailed description, in the following description, elaborate many concrete details so as to Understand the present invention in sufficient, but the present invention can be to be much different from the other manners of description to implement, therefore, the present invention Do not limited by the specific embodiment of following discloses.
The wide cut wide range LONG WAVE INFRARED Hyperspectral imager schematic diagram based on detector array shown in 1 with reference to the accompanying drawings, We provide specific embodiment party by taking airborne LONG WAVE INFRARED hyperspectral imager as an example, by the design feature in the present invention and function Method.Airborne long wave hyperspectral imager system index is as follows:
Flying height: 1Km;
Flying speed: 150Km/h
Ground resolution: 0.5m;
Breadth: 1Km;
Wave-length coverage:8.0~12.5 μm;
Spectral coverage number: 40;
Detector pixel dimension: 28μm
Due to airborne LONG WAVE INFRARED hyperspectral imager, thermal infrared radiation enters detection after being divided through beam splitting system Device end energy is weaker, in order to reach preferable detection efficient, must be requested that detector has larger detectivity and larger picture Elemental size.It disclosure satisfy that the face formation Long Wave Infrared Probe that airborne LONG WAVE INFRARED high light spectrum image-forming instrument system uses typically has Pixel dimension is 15 μm, and pixel number 640 × 512, and pixel dimension are 30 μm, and pixel number is 320 × 256 two kinds of specifications. Under the conditions of above-mentioned airborne LONG WAVE INFRARED hyperspectral imager system index, its angle of visual field can only achieve 137.2mrad, fly herein Under row height, ground breadth is only 128m, has larger gap with breadth 1Km in ground of the present invention resolution ratio.
According to above-mentioned technical indicator, as shown in fig. 6, aircraft flight is highly 1Km, aircraft flight speed is 150Km/h, ground Face resolution ratio is 0.5m, then one band imaging time of corresponding ground is 12ms.Therefore it is red 40 long waves must to be completed in 12ms The spectral scan of outer tunnel obtains with image.
With reference to the accompanying drawings 1, it is as follows to design the wide cut LONG WAVE INFRARED high light spectrum image-forming instrument parameter based on detector array:
The focal length of telephotolens 1 is 50mm;Bore 25mm, visual field are 60 °, and refraction type structure can be selected.
Compensated pendulum mirror 2 is quartzy speculum, and size is 150mm × 70mm × 20mm;Weight is about 460g.According to formula (1) and (2), slit 4 it is off-center away from ultimate range be 0.56mm, the displacement of slit 4 is ± 0.56mm;According to formula (1) offset angle of compensated pendulum mirror is ± 0.3102 °.
9ms is a cycle, and pendulum mirror motor meets with pendulum mirror motor control circuit:Drive compensated pendulum mirror 2 from- 0.3102 ° of stepping turns to+0.3102 °, and point 40 steps are completed, and it is 55.84 that each step, which rotates step-length, ";Driving is completed in 3ms to mend Repay pendulum mirror 2 and return quickly to -0.3102 ° of position.The load for putting mirror motor is 460g;Mirror motor is put to tilt from piezoelectric type Lens device, maximum deflection angle 5mrad, resolution ratio are 0.25 μ rad, and response frequency reaches as high as 1.5KHz.
The size of slit 4:W1=60mm;H1=28 μm;According to formula (2), the scanning range of slit 4 is ± 0.56mm;Slit 4 Machined using stainless steel substrates by the method for laser cutting, its weight is about 200g;
9ms is a cycle, and linear electric motors can meet with linear motor control circuit:Slit 4 is from -0.56mm step-scans To+0.56mm, point 40 steps are completed, per 0.028mm a length of step by step;In 3ms complete driving slit 4 be quickly back to- At 0.56mm.The load of linear electric motors is 200g.According to design, linear electric motors select the piezoelectricity straight line of big stroke high drive Dynamic device;Stroke 10mm, resolution ratio 1nm.
LONG WAVE INFRARED beam splitting system 5 can use Offner convex grating spectrometers, its axle enlargement ratio β=1.0 of hanging down;
LONG WAVE INFRARED hyperspectral imager composes the size of face 6:W2=56mm, H2=1.12mm;
Detector array 7 uses 2048 × 1 yuan of alignment mercury-cadmium-tellurium focal plane devices, and its size is:W3=56mm, H3=28 μ m;Single pixel dimension is:28μm×28μm.
Detector drives and acquisition of information circuit meets:In scanning process, the long wave of the target of 40 wave bands is obtained successively Infrared spectrum information.
The course of work of LONG WAVE INFRARED spectrometer based on detector array is as follows:As shown in fig. 7, to target imaging When, completed in 9.0ms:Slit 4 from -0.56mm step-scans to+0.56mm, complete by point 40 steps, per a length of step by step 0.028mm;The corresponding offset angle of compensated pendulum mirror 2 turns to+0.3102 ° from -0.3102 ° of stepping, and point 40 steps are completed, and each step turns Dynamic step-length is 55.84 ", while detector array 7 gathers 40 frame spectral image datas successively.Completed in 3ms:Slit 4 is quick - 0.56mm places are back to, compensated pendulum mirror 2 returns quickly to -0.3102 ° of position, starts the spectrum picture of next ground strips Obtain.The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, it is all the present invention spirit and All any modification, equivalent and improvement made within principle etc., should be included in the scope of the protection.

Claims (3)

1. a kind of wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array, including telephotolens (1), compensation Put mirror (2), imaging lens (3), slit (4), LONG WAVE INFRARED beam splitting system (5), LONG WAVE INFRARED spectrum focal plane (6), detector array (7), it is characterised in that:
Light from target is after telephotolens (1) convergence, and after being reflected by compensated pendulum mirror (2), imaged mirror (3) is imaged on On slit (4), by the emittance after slit (4) after LONG WAVE INFRARED beam splitting system (5), in LONG WAVE INFRARED spectrum focal plane (6) polishing wax is imaged, and recycles detector array (7) to obtain image information;Slit (4) moves up and down along vertical slits direction and swept Retouch, compensated pendulum mirror (2) synchronizes rotation sweep, the image planes of the different spectral wavelengths of same target is pressed in focal plane (6) position Wavelength size sequentially moves up and down, so that detector array (7) timesharing obtains the information of all wavelengths spectrum channel.
2. a kind of wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array based on described in claim 1 Imaging method, it is characterised in that:The LONG WAVE INFRARED Hyperspectral imager is mounted on motion platform (8) target is carried out Imaging, specific imaging method are as follows:
Slit (4) along vertical slits direction from deviate primary optical axis (1-1)Position divide N step step-scan to deviation Primary optical axis (1-1)Position, compensated pendulum mirror (2) is synchronous from deviateing main shaft (1-2)Position N is divided to enter rotation sweep step by step to deviation main shaft (1-2)Position, the picture of the different spectral wavelengths of same target Face divides N steps order mobile from the bottom up in focal plane (6) position by wavelength size, obtains N number of continuous spectrum segment information, detector array (7) its photoelectric conversion signal is read, so that detector array (7) timesharing obtains N in the whole LONG WAVE INFRARED wave-length coverage of target The information of individual spectrum channel, N are the spectral coverage number of the LONG WAVE INFRARED Hyperspectral imager;
Detector array (7) obtain the whole N number of passage of LONG WAVE INFRARED scope of target high spectrum image after, slit (4) quickly from Deviate primary optical axis (1-1)Position return to deviate primary optical axis (1-1)Position, corresponding benefit Pendulum mirror (2) is repaid quickly from deviation pendulum main shaft (1-2)Position return to deviate main shaft (1-2) Position, start to be imaged next target;The all wavelengths spectrum of target imaging needed for obtaining that repeats the above steps leads to The information in road;
Wherein, slit (4), which moves up and down, deviates the distance L of primary optical axis (1-1) positionnTurn the angle of scanning with compensated pendulum mirror rotation (2) αnRemain following relational expression:
<mrow> <msub> <mi>&amp;alpha;</mi> <mi>n</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mfrac> <msub> <mi>L</mi> <mi>n</mi> </msub> <mrow> <msub> <mi>D</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>D</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mo>-</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mfrac> <mrow> <mi>v</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>L</mi> <mi>n</mi> </msub> </mrow> <mrow> <mi>h</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>v</mi> <mi>L</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow>
Wherein, vLFor slit (4) movement velocity, v is motion platform (8) overall operation speed, and h is that motion platform (8) operation is high Degree;D1For the distance of telephotolens (1) and compensated pendulum mirror (2);D2For compensated pendulum mirror (2) and slit (4) distance.
3. a kind of wide cut wide range LONG WAVE INFRARED Hyperspectral imager based on detector array according to claim 2 Imaging method, it is characterised in that:The slit (4), which moves up and down, deviates the ultimate range scope of primary optical axis (1-1) position
<mrow> <msub> <mi>L</mi> <msub> <mi>n</mi> <mi>max</mi> </msub> </msub> <mo>=</mo> <mfrac> <msub> <mi>H</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mo>&amp;times;</mo> <mi>&amp;beta;</mi> <mo>,</mo> </mrow>
Wherein, H1For the height of LONG WAVE INFRARED spectrum focal plane (6), β is the vertical axle enlargement ratio of LONG WAVE INFRARED beam splitting system (5),
<mrow> <mi>&amp;beta;</mi> <mo>=</mo> <mfrac> <msub> <mi>H</mi> <mn>2</mn> </msub> <msub> <mi>H</mi> <mn>3</mn> </msub> </mfrac> <mo>,</mo> </mrow>
Wherein, H2For slit (4) height, H3For detector array (7) height.
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