Low-background large-aperture infrared measurement facility: design considerations

Low-background large-aperture infrared measurement facility:design considerations

Rudolf H. Meier and Alan B. Dauger

Design features of a measurement facility for the prelaunch evaluation of ir space sensors are described.

After a listing of the facility's major capabilities, an analysis of its internal calibration process is given. This

is followed by a discussion of test beam characteristics and some performance limitations. Concepts for im-

provements are presented.

Introduction

A prerequisite for the prelaunch testing of ir spacesensors is the realistic simulation of the low-radiationbackground of space. Against this background a well-collimated and uniform test beam is generated. Thetest beam's broadband irradiance must span a range ofat least 8 orders of magnitude, and its spectral compo-sition should be known at all irradiance levels. Thedetermination of the spectral responsivity of the sensorrequires the test beam to be converted into tunablemonochromatic flux over a wavelength interval fromabout 3 ,m to 32 im.

The test beam's radiometric properties must bemeasured and monitored with an internal dual-modespectroradiometer, which can function as either a ra-diometer or a scanning spectrometer. In both modesof operation, the calibration of the spectroradiometeritself is derived from an internal blackbody-type ref-erence source.

Basic Layout

The schematic layout of Fig. 1 illustrates the basicconfiguration of the interior of a recently completedportable low-background measurement facility. Thesource assembly can be converted from a broadbandradiator into a three-grating monochromator. Thecollimator is an unobscured 0.43-m diam off-centersection of a Cassegrainian system. Its effective focallength is 3.48 m. The test beam can be deflected abouttwo axes by two plane scan mirrors generating either adynamic scan or a stationary angular excursion of the

The authors are with McDonnell Douglas Astronautics Company,Huntington Beach, California 92647.

Received 14 October 1977.0003-6935/78/1115-3541$0.50/0.© 1978 Optical Society of America.

beam. The spectroradiometer can alternately be irra-diated by a portion of the test beam and by the referencesource. When functioning as a spectrometer, threediffraction gratings are activated. Detailed descrip-tions of both the source assembly and the spectroradi-ometer have been given previously. 1 2

In the next section, the facility's calibration processwill be described, followed by discussions of test beamcharacteristics and of some observed performancelimitations. In conclusion, concepts for improvementsare outlined. The actual initial performance of thefacility is discussed in detail in the following paper. 3

Calibration

The radiometric characterization of the test beam isobtained by comparing the signal it generates in thespectroradiometer with that generated by the referencebeam. The latter originates from the reference sourceand is expected to possess spectral properties similarto those of radiation emitted by a perfect blackbody, atleast at temperatures at or above 300 K. The calibra-tion flow diagram is shown in Fig. 2.

The signal generated by the reference beam in theradiometer yields the radiometer's broadband respon-sivity RSR (T) toward the reference blackbody's radiantoutput. Without prior knowledge of the relativespectral responsivity r'(X) of the radiometer, RSR (T) isof little practical value.4 With r'(X) known, the mea-sured value of RSR (T) permits the derivation of a con-stant quantity RSR' that yields the radiometer's abso-lute spectral responsivity. Writing

RSR(T) = V(T)G OR(T)

RSR' r'(X)0x(X,T)dX

(V W-1), (1)

S 0,(X,T)dX0

15 November 1978 / Vol. 17, No. 22 / APPLIED OPTICS 3541

The absolute spectral responsivity of the radiometertoward the reference blackbody's radiant output isobtained by forming the product

RSR'(X) = RsR'r'(X) (V W1) (3)

One obtains x(X,T), the spectral flux emitted by thereference blackbody at temperature T and aperture areaAR into the acceptance solid angle QR of the referencecollimator, by writing

I fl, f-AR~~ ) j0 J L(,A, T)dwdA (W nm-). (4)

Assuming the radiance L to be uniform over AR andwithin R permits the spectral irradiance of the refer-ence beam to be expressed as

Fig. 1. Low background measurement facility.

where r'(X) is the peak normalized relative spectral re-sponsivity of the radiometer, OR (T) = fO kO(X,T)dX isthe radiant flux emitted by the reference source into theacceptance solid angle of the reference collimator, G isthe gain of the amplifier, and V(T) is the signal voltage,yields

RSR' =V(T)

(V W-1)

G 5 r'(X)P,(XT)dX

Ex(?,T) =AR 2( MxG\,T) (Wcm-2,um-1),iFRC

(5)

where FRC is the reference collimator's focal length, E'(X)is the emissivity of the reference source, and Mx(X,T)is the spectral exitance of a Planckian radiator.

The only quantity not exactly known in Eq. (5) isE'(X), the effective spectral emissivity of the referenceblackbody assembly. It must be assumed that E'(X) notonly includes effects of possible spectrally dependentdepartures from unity of the emissivity E(X) of theblackbody cavity, but that it is also shaped by temper-ature gradients inside the cavity, by elevated temper-atures of the chopper and of the aperture wheel, and by

Fig. 2. Radiometric calibration flow diagram.

3542 APPLIED OPTICS / Vol. 17, No. 22 / 15 November 1978

diffraction at the aperture itself. A carefully designedreference blackbody may reduce or even completelyeliminate some or all of these effects, but this is difficultto verify in the absence of a recognized calibrationstandard. At this time, a significant inherent uncer-tainty remains in our knowledge of E'(X).

The signal generated by the reference beam in thespectroradiometer when operating as a spectrometer

V(X,T) = RSR(X)OX(X,T)AXSR (V).

1.0'

z.

- 0.5

-

g13:

(6)

Here, RSR (X) is the spectral responsivity of the spec-trometer, and AXSR is its half-intensity bandwidth.

The product RSR (X)AXSR characterizes the specificresponsivity of the spectrometer at given settings of itsentrance and exit aperture. It also includes the am-plifier gain. Inserting Eq. (5) into Eq. (6) yields

A SmC-._ X 1 0 m

0.150.05 0.1DISTANCE FROM CENTER (MRAD)

Fig. 3. One-dimensional convolution of finite source aperture withAiry disk pattern of point source. Aperture radius 0.05 mrad.

V(X,T)7rFRc (V W-' )RSR()AXR -ARASRE'(X)MX\(X,T)(VWgi,

(7)

where ASR is the clear aperture of the spectroradi-ometer.

After having determined the spectral responsivity ofthe spectroradiometer in its two modes, as defined inEqs. (3) and (7), the radiometric characterization of thetest beam can be accomplished.

With the source operating in its broadband mode, thegenerated irradiance of the test beam is

E (T) = S ESx(X,T)dX.

I-Uaz

Z 0.5

I-61

-J

(8)

The spectral irradiance is obtained by diverting a por-tion of the test beam into the spectroradiometer andperforming a spectrometer scan. This yields

E,x(XT) = VS(X,T)[RSR(X)AXsRASR]-l (W cm-2 Am-1 ). (9)

The irradiance within any given wavelength band B isobtained by integration:

BES(B,T) = Ex(XT)dX (Wcm-2). (10)

The irradiance EM(X,T) of a monochromatic testbeam is measured with the radiometer. Denoting themonochromator's half-intensity bandwidth with LXXM,

one obtains

EM(X,T) = EM,X(X,T)AXM

= VM(X,T)[RsR'r'(X)ASRG>-1 (W cm- 2 ). (11)

It should be remembered that RsR'r' (X) is the absolutespectral responsivity of the radiometer toward the ref-erence blackbody and, therefore, carries the latter'suncertainty in E'(X).

A somewhat tedious but quite useful experimentwould be the measurement of EM(X,T) with the spec-trometer. Because of the finer rulings of its threegratings, the half-intensity bandwidth IAXM of the mo-nochromator is only about one-half of the half-intensitybandwidth AXSR of the spectrometer, making AXM thedetermining quantity of the spectral purity of thespectrometer output. Thus,

0

=5pm

X= 15,um

X= 25pm

0.150.05 0.1DISTANCE FROM CENTER (MRAD)

Fig. 4. One-dimensional convolution of finite source aperture with

Airy disk pattern of point source. Aperture radius 0.018 mrad.

EM(X,T) = EM,x(X,T)AXM

= VMSP(G,T)[RSR(X)ASR_1 (W cm" 2). (12)

The quantity RSR(X) itself is not known. Thus, thismeasurement by itself would not yield EM(X,T), but itcould provide a check on the wavelength calibration andthe effectiveness of the order-sorting filters of the mo-nochromator and spectrometer and possibly an indirectdetermination of RSR (X)

Test Beam PropertiesThe collimation and the broadband and spectral

uniformity of the test beam, when formed by an aber-ration free optical system, depend on the collimator'sdiameter, on the size and shape of the source aperture,and on the spatial uniformity and geometry of the ra-diance passing through the source aperture.

Collimation

Diffraction at the collimator aperture makes a pointsource appear as an Airy disk. The angular diameterof its first dark ring is

(13)O = sin-' 244X 2.44X ,D) D


COUPLING-

E WHEEL

-RESOLVER

FLLTER-- WHEEL

SEGMENT

APERTUREWHEEL

INTEGRATING CAVITY

Fig. 5. Source assembly.

where D is the diameter of the collimator. A rigoroustreatment of diffraction effects on the collimation of abeam originating from a finite circular source involvesthe convolution of the aperture's cylindrical energydistribution with that of the Airy disk.5 Figures 3 and4 are plots of 1-D convolutions with two finite aperturesin the focal plane of a 0.43-m diam collimator. Theyshow clearly that, at longer wavelengths, the effectivesource diameter, as seen by the sensor, is significantlylarger than the geometric diameter.

The effect of small aberrations on the diffractionpattern is such that the apparent size of the disk and thepositions of the diffraction rings surrounding it remainsalmost unaltered; but the disk decreases in radiance andthe lost radiant energy reappears fairly broadly dis-tributed among the innermost diffraction rings. Fora point source, these effects are generally of littlepractical consequence, for the central disk still containsthe bulk of the radiant energy. However, larger aber-rations (e.g., a fourth-power aberration of one wave-length at mean focus) will send a further 17% of the ra-diant energy into the diffraction rings without changingappreciably the size of the disk or the relative intensitydistribution on it.6

The collimator had been specified to be diffraction-limited for wavelengths >5 gim. Thus, at X = 5 gim, the0.43-m diam collimator had to form an image spot ofabout 0.023-mrad angular diam. An angular blur of0.01 mrad, caused solely by aberrations of the two col-limator and the two scan mirrors, results in an effective

BLACKBODYCAVITY -

point source diameter of about 0.03 mrad, which wasconsidered acceptable. To achieve this, each surfacecould not contribute more than 0.005 mrad to the de-collimation. The maximum permissible slope of anydeparture from the ideal surface of any one of the fourmirrors was, therefore, 0.00125 mrad. Taken acrosstheir diameter, the resultant departure had to be ±0.54gim or about one wave in the visible region.

Beam UniformityThat significant errors can be caused in precise ra-

diometry by diffraction at any limiting aperture hasbeen shown by Blevin,7 who treated the case of a pointsource behind a circular diffraction aperture. Thetreatment of the theory was taken one stage further bySteel et al. 8 and by Boivin9 to include the case of a finitesource behind a circular diffracting aperture centeredon the axis of the aperture. This is directly applicableto the geometry of the facility's source assembly, which,for convenience, is shown in Fig. 5. Diffraction willoccur at the limiting aperture of the blackbody sourceand at the exit aperture of the integrating cavity, re-sulting in both spatial and spectral nonuniformities ofthe test beam.

How the source assembly's geometric configurationhas minimized these effects is illustrated in the opticalschematic of Fig. 6. It shows that, to balance diffractioneffects in the source assembly's relay beam, the black-body cavity diameter has been made significantly largerthan the effective blackbody aperture S. Also, the

COLLIMATORACCEPTANCERELAY OPTICS ANGLE

-INTEGRATINGCAVITY APERTURE

DIFFRACTED OUT

Fig. 6. Schematic of source optics minimizingdiffraction effects.


MIRROR/GRATINGBLOCK

BOLOMETERTELESCOPE

X g < REFERENCE BEAMOR FROM TEST BEAM

g ' t\ l FILTER WHEEL

Fig. 7. Presently existing spectroradiometer configuration.

CM

4.01

A(F.L.)

x

A(B.F.)

0.25 0.5

% INCREASE IN

0.75 1.0

RADIUS OF CURVATURE

Fig. 8. Increase in focal length and change in back focus position as

function of percentage increase in radius of curvature of primary.

REFERENCE SOURCE

MIRROR/GRATINGBLOCK

DETECTORASSEMBLY

I TEST BEAM I

I REFERENCEI COLLIMATOR

I\

TOP VIEW

Fig. 9. Schematic of modified spectroradiometer with referencesource assembly.

latter has been positioned close to the cavity. Thesetwo design features ensure that about equal amountsof radiant flux are diffracted into and out of the sourcerelay optics bundle. Similar considerations are validfor the radiant flux emerging from the integrating cavityaperture S'. For this reason, the relative aperture ofthe collimator was chosen to be only half of the sourcerelay system.

Performance Limitations

Two performance limitations were observed, bothinvolving the spectroradiometer (Fig. 7). The spec-troradiometer's first optical subsystem, a Cassegrainiantelescope, accepts either a deflected portion of the testbeam or the reference beam and forms an intermediateimage of the test source or reference source at thelocation of the entrance aperture of the spectrometer.This telescope was the cause of a degradation of thespectroradiometer performance which was difficult torectify. The degradation was caused by a surface de-formation of its primary mirror at cryogenic tempera-tures resulting in a 0.6% increase of its radius of curva-ture. The deformation arose from the difference be-tween the thermal coefficients of expansion and themoduli of elasticity of the aluminum blank and theKanigen (mainly nickel) layer that was firmly appliedto its reflecting surface.10 The practical consequencewas an increase of the effective focal length and a shiftof the back focus position of the telescope. Figure 8 isa plot of the change in focal length and of the back focusdisplacement in centimeters as a function of the percentchange of the primary's radius of curvature. 11 It showsthat a 0.6% increase in the radius of curvature will resultin 2-cm increase in the telescope's effective focal lengthand a 1.1-cm shift of its back focus position. This isquite significant but in good agreement with the ob-served shift during the first operational pump-downsof the facility. Also, by overfilling the secondary, theprimary's distortion reduced the telescope's effectiveaperture, causing an otherwise avoidable uncertaintyin the over-all calibration.

Another performance limiting property of the spec-troradiometer was its moderate SNR caused by therelatively low sensitivity of its bolometer-type detectorand the unavoidable losses in the grating spectrometer.Two proposed modifications, intended to overcome thediscussed difficulties, will be outlined in the followingsection.

Proposed Improvements

The conceptual layout of a more thermally stable andmuch simplified three-grating spectroradiometer ispresented in Fig. 9. Its size and arrangement arecompatible with the space occupied by the existingspectroradiometer. The troublesome Cassegrainiantelescope is eliminated, and the number of reflectionsreduced from eight to three which should greatly in-crease the accuracy of r'(X), the peak normalized relativespectral responsivity of the radiometer. To increase itssensitivity, the bolometer-type thermal detector shouldbe supplemented by one or several high sensitivityphotoconductive devices. The latter's responsivitiesare wavelength dependent, but this should be of minorconcern in this application.

Another novel and more far-reaching improvementof the facility would be replacing the existing gratingspectrometer by a Fourier transform spectrometer withits superior light-gathering power and multiplex ad-vantage.12 If some of the involved technical difficulties,


3.01-

2.01-

1.01-

e.g., the manufacture of a stable beam splitter for theentire wavelength interval and the implementation ofa precise scan motion at cryogenic temperatures can besolved, an instrument of this type should be consideredattractive for low-background spectroscopy.

Conclusion

The internal calibration process and some selecteddesign features of a recently completed low-backgroundlarge-aperture portable measurement facility for pre-launch evaluations of ir space optical systems have beendiscussed. Fundamental limits to its test capabilitiesare set by our knowledge of E'(X) of the internal radiationstandard and by diffraction induced properties of thebeam. Observed and to some extent correctable limi-tations were caused by marginal SNRs of the spec-trometer output at low irradiance levels and by a me-chanical instability at cryogenic temperatures of one ofits optical subsystems. A detailed account of the initialperformance of the facility is presented in the followingpaper. 3

This work was performed under U.S. Army contractDAHC60-73-C-0096. The views and conclusions con-tained in this document are those of the authors andshould not be interpreted as necessarily representingthe official policies, either expressed or implied, of theU.S. Army.

The authors thank B. L. Walker of BMD-ATC,Huntsville, Alabama, for a constructive review of thispaper. Thanks are also due to J. E. Gallagher forcomputations dealing with effects of surface deforma-tions and for generating the convolution plots and to I.Richman for valuable discussions on diffraction effectsand Fourier spectroscopy.

References

1. R. H. Meier, Appl. Opt. 14, 1021 (1975).2. R. H. Meier and A. B. Dauger, Opt. Eng. 14, SR-144 (1975); 14,

SR-182 (1975).3. R. H. Meier and A. B. Dauger, Appl. Opt. 17, 3547 (1978).4. The determination of the relative spectral responsivity of the

radiometer r'(X) must be performed prior to actual chambercalibration. It consists of two measurement operations. Oneis the determination of the spectral dependence of the reflectanceof the radiometer's optical surfaces or, if this is not practical, ofidentically manufactured sample surfaces. To exclude errors thatcould arise from a possible temperature dependence of thisquantity, the measurement should be performed with the mea-sured samples at a temperature of about 25 K. The secondmeasurement operation is the determination of the detector'srelative spectral responsivity r(X). The setup for this measure-ment should duplicate the beam incidence geometry of the ra-diometer. Both measurement operations must be carried outover the entire wavelength interval of nonzero detector respon-sivity.

5. R. C. Jennison, Fourier Transforms and Convolutions for theExperimentalist (Pergamon, Oxford, 1961).

6. E. H. Linfoot, Fourier Methods in Optical Image Evaluation(Focal Press, London, 1964).

7. W. R. Blevin, Metrologia 6, 39 (1970).8. W. H. Steel, M. De, and J. A. Bell, J. Opt. Soc. Am. 62, 1099

(1972).9. L. P. Boivin, Appl. Opt. 15, 1204 (1976).

10. R. Chen, "Curvature of Composite Plate Due to Thermal Con-traction," Informal McDonnell Douglas Astronautics Co. Com-munication (1976).

11. J. E. Gallagher, "Analysis of Spectroradiometer Telescope withPAGOS Program," Informal McDonnell Douglas AstronauticsCo. Communication (1976).

12. A. P. Thorne, Spectrophysics (Chapman and Hall, London, 1974),Chap. 5 and 6.

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Low-background large-aperture infrared measurement facility: design considerations