NASA Technical Paper 1504

Spatial-Frequency Response of the Limb Infrared Monitor of the Stratosphere

R. Gale Wilson, Antony Jalink, Jr., and William M. Kahlbaum, Jr.

AUGUST 1979

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https://ntrs.nasa.gov/search.jsp?R=19790021508 2020-06-07T19:05:21+00:00Z

TECH LIBRARY KAFB, NM

NASA Technical Paper 1504

Spatial-Frequency Response of the Limb Infrared Monitor of the Stratosphere

R. Gale Wilson, Antony Jalink, Jr., and William M. Kahlbaum, Jr. Latzgley Research Ceuter Havzptopz, Virginia

National Aeronautics and Space Administration

Scientific and Technical Information Branch

1979

SUMMARY

The Limb Infrared Monitor of the Stratosphere (LIMS) is one of the experi- ments on the Nimbus-7 satellite. It is designed to scan the Earth's limb ver- tically and to measure spectral emission profiles of trace atmospheric gases that are believed to be important in processes controlling the stratospheric ozone distribution. The LIMS must have adequate spatial-frequency response for all the spectral channels to provide, through inversion of the measured limb radiance profiles, important information about the temperature, structure, and composition of the atmosphere. Experiment objectives are reviewed and several analyses and measurements are described which were performed to determine the adequacy of the system for satisfying these objectives. From the LIMS design- model data, the modulation transfer function (MTF) was calculated for the optical system, the detector field mask, the electronics, and the overall system for each channel. The signal output performance of the instrument was predicted from the system MTF data and model input radiance data for each chan- nel. The MTF measurements made on the flight sensor confirmed the analytical results. The predictions indicate that the instrument can satisfy the basic measurement objectives of the experiment.

INTRODUCTION

The experiment Limb Infrared Monitor of the Stratosphere (LIMS), launched aboard the Nimbus-7 spacecraft in 1978, is designed to scan the Earth's limb vertically and to measure spectral emission profiles of trace atmospheric gases that are believed to be important in processes controlling the stratospheric ozone distribution. The limb radiance profiles of these gases (i.e., the spatial variation measured as the radiometer scans from the Earth's disk across the atmosphere) can be inverted (refs. 1 and 2) to provide important information about the temperature, structure, and composition of the atmosphere. The LIMS measures the radiance profiles of ozone (O3), water vapor (H20), nitrogen dioxide (N02), nitric acid (HNO3), and carbon dioxide (C02). The LIMS is one of several planned instruments (ref. 3) for surveying the atmosphere on a global scale and for obtaining an improved understanding of the physical and chemical relationships affecting its functions. The limited knowledge of the distributions of the gases within the atmosphere that LIMS will be measuring is due to natural variations such as latitude, season, and time, and to anthro- pogenic activities. For example, reference 4 provides a good survey of such variations for H20.

The specific experiment goals, system operation, and data-processing elec- tronics of LIMS have been described in reference 5. The present paper elab- orates on the spatial-frequency response characteristics of the LIMS and relates them to model radiance profiles of the type that the LIMS instrument is expected to observe. The limb-scanning technique used in the LIMS experi- ment, ccanbined with the exponential falloff of atmospheric emission with alti- tude, provides an inherently high vertical-resolution potential (ref. 1 ) .

Design and performance trade-off typically includes field of view, signal to noise, target radiance, instrument collection aperture, and spectral range, as well as science requirements.

After a brief review of the LIMS experiment objectives, the associated radiometric requirements and the analytical methods used to verify the optical- system design model are presented. Then analytical spatial-frequency response (modulation transfer function) data on the design model and the measured response data on the f l ight sensor are discussed. Finally, a brief assessment of the expected performance of the LIMS system is given, based on predicted inputs and on the system performance analysis.

Throughout the LIMS system analysis, the authors relied upon the com- putational expertise of William L. Edmonds, Systems and Applied Sciences Corporation.

Use of trade names or names of manufacturers i n t h i s report does not con- s t i t u t e an of f ic ia l endorsement of such products or manufacturers, ei ther expressed or implied, by the National Aeronautics and Space Administration.

LIMS EXPERIMENT OBJECTIVES

Measuring the stratospheric ozone distribution is the primary objective of LIMS. A typical radiance profile for 03 has been synthesized from studies reported i n references 6 and 7 and from related studies supporting the develop ment of LIMS and ear l ier limb-scanning experiments (refs. 8 and 9 ) . Typical radiance profiles have also been synthesized for H 2 0 , HNO3, N02, and C02. The C02 radiance data, by virtue of t h e known uniform distribution of CO2, allow determination of the atmospheric vertical temperature profile needed for inver- sion computations. Carbon dioxide has been extensively modeled from temperature and pressure profiles representing temporal, geographical, and meteorological variations over the Earth's surface (refs. 6 and 7 ) . These models account for the absorption of water vapor and ozone i n the outer portions of the C 0 2 spec- t r a l band. Representative radiance profile models for t h e gases that LIMS measures are shown i n figure 1 . For the purposes of t h i s paper, the spatial- frequency contents of the radiance profiles are primarily of interest (i.e., their Fourier spectra, estimations of which are shown i n fig. 2 ) . The radiance profiles are synthesized from 64 data points which correspond to l-km incre- ments of altitude: therefore, the maximum spat ia l frequency for which the spectra are determined is 0.5 cycle/km. It is seen that for al l the profiles, the amplitude spectrum decays over the range defined by two or more orders of magnitude relative to the zero-frequency amplitude. The spectra were estimated by applying discrete Fourier transform techniques to the radiance profiles, a f te r f i r s t multiplying the profiles by the Hann windowing function (ref. 1 0 ) , followed by frequency averaging or smoothing (ref. 1 1 ) .

The LIMS experiment seeks to provide radiance measurements w i t h a 12-b i t (4096-level) amplitude resolution and with an error not greater than f l per- cent for constant radiance (dc) targets. I n addition, the measurements should have sufficient resolution to follow atmospheric features w i t h a period as short as 5 km i n a l t i tude (i.e. , a spatial frequency of 0.2 cycle/km a t the

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atmospheric target for four narrow instantaneous fields of view ( I F o V ' s ) and 0.1 cycle/km for two wide IFOV's ) . However, it is desirable that the instru- ment have the capability to respond to features of shorter period to determine whether they are present.

L I E RADIOMETRIC SYSTEM

Figure 3 is a schematic of the LIMS optical system. The optical-system design was determined from a combination of resolution requirements, signal-to- noise constraints, and canpatibility requirements se t by the two-stage cryogenic cooler for the detectors (ref. 5 ) . The system has three focal planes to satisfy the thermal and optical requirements. The f i r s t is located a t the focus of the primary paraboloidal collector mirror, coincident wi th the chopper and calibra- tion source (not shown i n fig. 3 ) . The second focal plane coincides with a thermal mask that is important i n the cryogenic cooling requirements. The f inal focal plane contains band-pass f i l t e r s , the field-def ining stop, and the detec- tors. The following optical-system studies that are described relate to the final focal plane.

Figure 4 shows the shape of the field-stop mask and the corresponding detector array. The s i x detectors (four narrow and two wide) are located immediately behind the field stop. The detector dimensions are s l i g h t l y larger than the field-stop apertures, so that al l radiation w i t h i n each IFOV is col- lected. The spectral band-pass f i l t e r s a r e mounted on the front of the field stop. The atmospheric constituent corresponding to each detector is shown, as well as the wavelength value for each channel which was used i n the optical- system analysis. Each wavelength i n figure 4 is the midpoint of the LIMS channel spectral response. Because of the narrow spectral response of each LIMS channel , t h i s midpoint corresponds essentially with the effective wave- length (centroid). Additional details of the LIMS optical system that are needed i n the analyses are presented i n appendix A.

The LIMS w i l l determine the vertical distributions of stratospheric 03, N02, HNO3, H20, and temperature with resolutions of about 1 km for temper- ature, 03, and HNO3, and of about 2 km for NO2 and H20. The C02 radiance pro- fi les for the two pass bands become data input to inversion algorithms to determine the vertical temperature profile of the atmosphere (refs. 1 and 2) . The inferred temperature profile is coupled wi th radiance data for the other gases to provide the distribution (density profile) of N02, H20, 03, and HNO3. The alt i tude ranges for measurements are from the troposphere to 75 km for temperature, to 6 4 km for 03, to 50 km for H20, and to 40 km for HNO3 and N02.

SPATIAL-FREQUENCY RESPONSE ANALYSIS

The prediction and evaluation of electro-optical systems performance by optical transfer function (OTF) techniques are now recognized procedures (ref. 1 2 ) . The OTF calculations (predictions) based on the design parameters were performed for the LIMS optical system w i t h two different computer pro- grams for field angles corresponding to the geometric centers of the detec- tors. The two programs are POLYPAGOS (ref. 13) and ACCOS V (ref. 1 4 ) . Before

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comparative OTF calculations were done, agreement was established between the two programs for a paraxial ray-trace t e s t case. For convenience, appendix B presents a brief tutorial on the analytical methods basic to these computer programs.

The OTF calculations for the LIMS optical system were made for the direc- tion across the narrow dimension of the detector (i. e., along the vertical scan direction of LIMS). The modulation transfer function (MTF) data for two typical channels (03 and H 2 0 ) of the LIMS that represent the two different IIXlV's are shown i n figures 5 and 6. The agreement between the two se ts of independent LIMS (optics) MTF calculations appears consisent wi th the current s ta te of the computational a r t for complex optical systems. (See appendix B.) The phase transfer function (PTF) is shown for a l l the channels i n figure 7. The MTF data are presented for the range of spatial frequencies of primary interest i n the LIMS application. More complete data are included i n appen- d i x C. "Wo spatial-frequency scales, cycles/mrad and cycles/mm, are shown. The two scales are related by

cycles 1 cycles

mrad f m - x - x 1 ~ 3 = -

where f is the focal length (1 57 mm) of the optical system. Later these spatial-frequency scales w i l l be related to the cycles/km (at target) , scale, i n which performance requirements were specified.

The M T F curve for the HNO3 channel (appendix C) is nearly the same as that for 0 3 . The MTF curves for the CO2 channels (appendix C) are similar i n shape to, but somewhat lower i n magnitude than, the 0 3 curves over most of the frequency range. The MTF curve for the No2 channel (appendix C) d i f fers very l i t t l e from that for the Hz0 channel over the frequencies of most significance.

Appendix D presents methods used to define the best focal plane of the LIMS optical system. A l l the OTF data correspond to the best focus.

The overall system response function for each channel is defined by the product of ( 1 ) the optical transfer function, (2) the response characteristic due to the geometric subtense of the IFOV stop, and ( 3 ) the response of the f i l t e r i n the signal-processing electronics. Figure 8 shows the predicted LIMS total electro-optical system M T F for the 0 3 channel. I n t h i s figure, the curve designated MTF(0) is the optical system "F, taken from figure 5 (ACCOS V data). The MTF(S) curve represents the field-stop (detector-slit) contribution, given by the relationship (normalized)

s i n (@f)

TBf MTF(S) =

4

where B is half the IFOV (mrad) and f is the spatial frequency (cycles/mrad). The curve designated MTF(F) represents the response of the four-pole Butterworth f i l t e r , which provides a cutoff (3-dB) frequency of 4 . 4 Hz for the ozone channel, as well as for the CO2 and HN33 channels.

For convenience, the frequency scale is given i n three different u n i t s . The temporal-frequency scale (Hz) is related to the angular spatial-frequency (cycles/mrad) scale by the relationship

cycles/mrad cycles/mrad HZ = - -

scan rate (mrad/sec) 4.36 mrad/sec

The third frequency scale (cycles/km) is related to the cycles/mrad scale by the fact that 1 km a t the target (Earth's horizon) subtends 0.286 mrad a t the radiometer for the nominal orbital al t i tude of 900 km

cycles cycles x 0.286 mrad

km (at target) mrad km (at target) - -

The MTF coordinate is shown over a range of three decades. The two scales are related by

dB = 20 log (MTF) (5)

Figure 9 presents corresponding predicted LIMS total-system data for the H z 0 channel. (See appendix C for similar results on the other four channels.) The detector-slit transfer function for the H20 channel has a lower cutoff than that for the 0 3 channel since the slit width for the H20 channel is twice that for the 0 3 channel. Also, the cutoff frequency of the electronics-filter func- tion for the Hz0 channel (NO2 channel also (see appendix C ) ) is a t a value one- half (i.e., 2 . 2 Hz) that for the 03 channel (C02 and HNO3 channels also). The overall system response for the NHO3 channel is practically identical w i t h that for 0 3 , and the system responses for the C02 channels differ insignificantly from the 0 3 channel response. I n addition, the NO2 channel system response is practically identical wi th the H S channel response.

The dashed portions of the f ield-mask (slit) M T F curve (f igs . 8 and 9) and of the system M T F curve represent the so-called "spurious resolution" regions of the system behavior beyond the f i r s t zero crossing of the field- mask transfer function. I t is seen that the spurious resolution occurs a t spatial frequencies greater than 0.57 cycle/km for the 0 3 (C02 and HNO3) channel and greater than 0 .29 cycle/km for the H z 0 and NO2 channels. The values of 0.57 and 0.29 cycle/km i n the object (target) plane correspond to the values of 2 cycles/mrad and 1 cycle/mrad, respectively (i.e., the first

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z e r o p o i n t s i n t h e slit t r a n s f e r f u n c t i o n s ) . The LIMS "I? ( spur ious) beyond t h e s e two spa t ia l f r equenc ie s is down by a t least t h r e e orders of magnitude r e l a t i v e to the zero-frequency MTF.

The c o n s i d e r a t i o n s i n c h o i c e of t h e e l e c t r o n i c s - f i l t e r pass band are two- fold. On the one hand , t he cu to f f is chosen to pass a l l s igna l f r equenc ie s expected to be important. On the o the r hand , i n t he sampled data system used i n LIMS ( r e f . 5), t h e l o c a t i o n of t h e 3-dB f r equency , t oge the r w i th t he steep- ness provided by four poles, mitigates a n y a l i a s i n g error, as i l l u s t r a t e d f o r t h e 03 c h a n n e l i n f i g u r e 10. The f i g u r e shows t h e o v e r a l l M T F for the 0 3 chan- n e l folded a b o u t the sampling f requency of 41.7 Hz t h a t is imposed by t h e LIMS Nimbus-7 data system. The logarithmic frequency scale distorts the mirror image. T h i s f i g u r e i n d i c a t e s t h a t a l i a s i n g errors are below t h e LIMS accuracy and r e so lu t ion r equ i r emen t s s ince the ove r l ap is nea r ly fou r o rde r s of magnitude below the zero-frequency response.

F igure 1 1 shows the phase r e sponse o f t he ove ra l l LIMS system for a l l t h e channels. These curves reflect mainly the phase response of the But te rwor th f i l t e r s i n c e t h e PTF of the optical system itself ( f ig . 7) is nea r ly ze ro for most of the channels over most of the frequency range.

MEASURED FREQUENCY RESPONSE

The ampl i tude responses o f the LIMS radiometric c h a n n e l s ( f l i g h t s e n s o r ) were measured by using a series of input square waves of constant amplitude and d i f f e r i n g f r e q u e n c i e s . The test s e t u p is s k e t c h e d i n f i g u r e 12 . A series of thermal bar t a r g e t s , c o n s i s t i n g of a l t e r n a t i n g h e a t e d and cooled metal bars, was placed i n t h e f o c a l p l a n e o f t h e test collimator. The cooled p o r t i o n o f the t a r g e t (back plate) was kept a t l iqu id-n i t rogen temperature to maintain the requi red cons tancy of input amplitude. The temperature of t h e warm p o r t i o n s (plate wi th slots) was c o n t r o l l e d a t 300 f 1 K by means of a c i r cu la t ing ba th . The measured data on t he LIMS 03 channel show some typical r e s u l t s .

The response measured by means of t h e c o n f i g u r a t i o n shown i n f i g u r e 1 2 is t h e square-wave response rather than the more convent iona l ( s inusoida l input ) MTF. The two responses can be compared by Four i e r ana lys i s . The response of the channel to the i npu t squa re waves can be best understood by cons ider ing the fo l lowing th ree f requency reg ions .

(1 ) For square-wave input f requencies f rom 0 to about 0.01 cycle/mrad, the 0 3 channel responds with l i t t l e amplitude and phase d i s to r t ion . The re fo re , t he o u t p u t c l o s e l y resembles the i npu t squa re wave. F igure 8 shows t h a t t h e t h i r d and f i f t h harmonics suffer hardly any decrease i n amplitude. Figure 11 shows t h a t t h e p h a s e s h i f t s for the t h i r d and f i f t h harmonics of t h e 0.01 cycle/mrad square wave wi th respect to the fundamental are about 1 3 O and 25O, r e spec t ive ly .

( 2 ) For square waves i n t h e r a n g e from 0.01 to 0.5 cycle/mrad, t h e o u t p u t is distorted by increased phase shif ts between the fundamental and harmonics . The p h a s e s h i f t s are caused mainly by t h e B u t t e r w o r t h f i l t e r . P h a s e s h i f t s close to 180° between the fundamental and harmonics cause the resul tant output wave to resemble a squa re wave wi th humps superimposed on it. The r e s u l t is

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(3 ) For input frequencies greater than 0.5 cycle/mrad, the phase s h i f t between the fundamental and harmonics decreases rapidly wi th increasing spatial frequency, b u t here the effects of steeply falling LIMS amplitude (sinusoidal) response suppress contributions of these harmonics almost completely. Conse- quently, for the higher frequencies, the output is a nearly sinusoidal response (i.e., a sinusoidal output is obtained for a square-wave input).

The measured responses representing the three frequency regions previously discussed for the LIMS 03 channel are shown i n figure 13. The expected dis- tortions discussed are apparent i n these measurements. The LIMS output response was characterized by determining the peak-to-peak amplitude of the output waves, which was then divided by the response for a zero-frequency target. These results are shown i n table I for a l l the LIMS channels for spatial frequencies fran 0 to 1.2 cycles/mrad.

The peak-to-peak measured square-wave response data for the ozone channel, corresponding to the data i n table I, are shown i n figure 1 4 as a series of circles. The solid-line curve, reproduced from figure 8 , is the M T F predicted for the 03 channel from design data. The dashed curve represents the peak-to- peak square-wave amplitude response predicted from the ozone channel by the Fourier analysis considerations previously described. Peaking of the dashed curve i n the midfrequency range occurs because of superposition and relative phase s h i f t s of the squarewave harmonics. The measured response reflects a small increase i n the midfrequency range, consistent w i t h that predicted for square-wave inputs, and then a gradual decrease to sinusoidal-output behavior. However, the measured data (circles i n f i g . 1 4 ) are below the predicted square- wave response curve, consistent wi th the fact that system manufacturing and alignment errors would be expected to reduce the performance as compared wi th that of idealized predictions. The channel retains close to 30 percent of the zero-frequency response a t the 1 / ( 2 x IFOV) frequency (1 cycle/mrad) to reflect the proper trade-off wi th field-mask (sl i t) dimensions.

PREDICTED FOURIER SPECTRUM OUTPUT AMPLITUDE

To obtain the predicted output of LIMS for each channel, normalized to the zero-frequency output, the following relationship is used:

Output spectrum = MTF(L1MS) x input spectrum ( 6 )

This relationship applies because there is a spatially incoherent radiance input t o the optical system (including field mask) which linearly maps object radiance into image irradiance at the detectors. The electronic system, i n turn, linearly maps the irradiance into a voltage output, i ts transfer function being that of the Butterworth f i l t e r ( f igs . 8 and 9 ) .

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Figure 15 presents the predicted normalized LIMS Fourier spectrum output amplitudes for a l l channels of the radiometer as determined from equation (6) (i.e., from multiplying the calculated M T F by the predicted input spectrum amplitude for each channel (fig. 2 ) ) . These predictions indicate that, for the H20 and NO2 channels, the output spectrum magnitude (relative to the zero- frequency output) a t 0.286 cycle/km, where the resolution becomes spurious, would be less than 1 O-5. For the 03 and HNO3 channels, the output spectrum magnitude a t 0.572 cycle/km, where the resolution becomes spurious, would be about 2 x and l om5, respectively. The C02 channel output a t 0.572 cycle/km appears t o be less than because its spectral falloff is faster than that for the other narrow IFOV channels. These predicted outputs are based on some extrapolation beyond the spectral range of the input-spectrum calculations, as indicated by the dashed parts of the curves i n figure 15, The implications are that any spurious resolution would be indistinguishable from noise unless the system could accurately quantize more than 50 000 radiance levels.

As stated earlier, the LIMS experiment seeks to provide radiance- measurement capability, wi th an amplitude resolution of 1 2 b i t s , a t spa t ia l frequencies a t the atmospheric target up to 0.2 cycle/km for the narrow IFOV'S and up to 0.1 cycle/km for the wide IFOV's. Nominal variations of the instru- ment temperature i n orbit cause changes i n the self-radiation of the optical system, to which the infrared detectors are sensitive. To prevent possible saturation of the channels due to variations i n the optical-system radiation component, the full-scale radiance excursion (midrange) of each channel is se t to 80 percent of the f u l l 12-bi t (4096-level) data-system range or to 3276 quan- tization levels (counts). Therefore, the operational requirement on amplitude resolution becomes one part i n 3276, or 3.1 x 1 0-4, up to 0.10 cycle/km for the NO2 and H z 0 channels, and up to 0.20 cycle/km for the 03, C02, and HNO3 chan- nels. As seen i n figure 15, the predicted LIMS output magnitudes a t these spatial frequencies, normalized to zero-frequency out u t , are 5.4 x for NO2, 4.3 x for H20, 2.6 x for 03, 4.1 x for C02, and 3.1 x €or HNO3. Therefore, the predicted outputs for a l l the channels are greater than the required amplitude resolution a t the highest spatial frequencies of interest by factors ranging from s l i g h t l y more than 1 for the C02 channel t o 174 for the No2 channel. These predicted outputs indicate the LIMS performance is adequate, provided the noise levels for a l l the channels are also less than the required amplitude resolution. Data that have become available since the October 1978 launch of Nimbus-7 (personal communication wi th John C. Gille, National Center for Atmospheric Research, and James M. Russell 111, Langley Research Center, who were principal co-investigators for the LIMS experiment) show the typical noise levels relative to the maximum channel range are 3 .8 x l o m 4 for N 0 2 ; 4.2 x for H 2 0 ; 4.6 x for 03; 8.9 x for C02(wide) ; 3.6 x 1 Om4 for C02(narrow) ; and 7.0 x 1 0'5 for HNO3. The noise levels represent the total spatial-frequency bandwidth of each channel. The noise levels appropriate to the 0.1 0 cycle/km (No2 and H20) and the 0.20 cycle/km (03, C02, and HNO3) frequencies would be much further reduced by the effects of the electronics M T F on the noise spectrum.

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CONCLUDING REMARKS

Experiment objectives of the Limb Infrared Monitor of the Stratosphere have been reviewed and related to its predicted and measured spatial-frequency response. Consideration of the predicted output signal spectrum and the flight-observed noise levels together indicates very favorable signal-to-noise characteristics up to the highest significant spatial frequencies.

Langley Research Center National Aeronautics and Space Administration Hampton, VA 23665 June 8 , 1 979

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APPENDIX A

LIMS OPTICAL SYSTEM

Figure A1 repeats t h e LIMS opt ical-system schematic shown i n f i g u r e 3 bu t breaks it i n t o t h r e e parts to show a l l the impor tan t cons t ruc t ion parameters needed f o r t h e optical t r a n s f e r f u n c t i o n (OTF) ca l cu la t ions . F igu re A1 (a) shows t h e f r o n t - e n d e l e m e n t s , i n c l u d i n g t h e f i r s t l e n s , a n d f i g u r e A1 (b) shows, the remainder of t h e s y s t e m , w i t h t h e f i r s t l e n s a lso included. Figure A l ( c ) shows details of t h e l a s t l e n s i n the system and of the focal-plane assembly (i.e., t h e spectral f i l t e r s , f i e ld mask, and detectors). The f i e l d mask t h a t d e f i n e s t h e i n s t a n t a n e o u s f i e ld of view (IFOV) €or each channel was shown i n f i g u r e 4. The view of t h e f i e ld mask shown is a l o n g t h e o p t i c a l a x i s 2 (i.e. , perpendicular to the v i ew in f i g . A1 (c) ) . The field-mask configura- t i o n is symmetric about the X- and Y-axes.

Table A I shows the r e f r ac t ive i ndexes a t t he appropr i a t e t empera tu res (see f i g . 3) and wavelengths for the CdTe lenses and window and for t h e G e sub- trates o f t he spec t r a l band-pass f i l t e r s . These i ndex data, a long with the temperature data i n f i g u r e 3 and t h e i n f o r m a t i o n i n f i g u r e s 4 and A1 , provide a l l t h e n e c e s s a r y i n p u t s f o r c a l c u l a t i n g t h e OTF of a l l channels of LIMS.

TABLE AI .- INDEX OF REFRACTION

Wavelength, I.lm

6.21 (N02)

6 . 8 3 (H20)

9 . 6 4 (03)

11 .32 (HN03)

1 5 .20 ((202 wide)

15.23 (CO2 narrow)

F Index o f r e f r ac t ion for - CdTe(1rtran-6) ' a t temperature, K , of -

297.5 152

2.68499

2.64390 2.65751

2.64390 2.65751

2.65755 2.671 39

2.66236 2.67621

2.669533 2 .68332

2.671 15

65

2.66288

2.661 294

2.65409

2.64927

2.63575

2.63575

~

G e a t 65 K

3.91 743

3.91 5565

3.91 131

3.91 028

3.90934

3.90934 ____

' I r tran-6: Registered trademark of Eastman Kodak Company.

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4 49*403 * View before

folding mirror

Y

Z

Vertex radius of

r Radius of curvature: 6.7899 \ - n- 14.2804

Radius of curvature:

u' 1.6764

*31751 F- 7.9370

Y *4473d le .2537 *313+

5.0696 "1, 4.8161 --d

(b) Outpu t end.

Figure A1.- Continued.

APPENDIX A

Y

Detector

curvature:

-Radius of curvature:

F i l t e r s

.4191 .3429

Fi l t e r

plane)

Fi l ter Fi l ter thickness 0.07453

0 .07833 0

/ / HN03 .07595

/

C02(Wide) .06251 C02(Narrow) .06251

N02 .07620

.21986 (03)

.22225 (HN03)

.23569 (C02 (Wide))

.23569 (C02 (Narrow))

(c) Focal-plane assembly.

F igure A1 .- Concluded.

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APPENDIX B

ANALYTICAL METHODS FOR OPTICAL TRANSFER FUNCTION CALCULATIONS

Al though t he ca l cu la t ion of t h e optical t r a n s f e r f u n c t i o n (OTF) from optical des ign parameters is, i n p r i n c i p l e , a s t r a igh t fo rward matter, many approximations and simplifying assumptions are r e q u i r e d , i n practice, to make the numer ica l ca lcu la t ions manageable . Di f fe ren t ana lys t s and des igners make d i f f e r e n t compromises i n t h e i r computer programs and generally get somewhat d i f f e ren t r e su l t s . On ly r ecen t ly have t hese d i f f e rences been well enough understood to provide good agreement between r e s u l t s o b t a i n e d by d i f f e r e n t eva lua tors and to assure good r e p r o d u c i b i l i t y among r e s u l t s of an i nd iv idua l eva lua to r ( r e f s . 12 , 15, and 1 6 ) .

POLYPAGOS Cmputer Program

POLYPAGOS ( c u r r e n t l y named t h e Spectral Lens Analysis Program (SLAP) and developed by the Pagos Corporat ion) is a general-purpose program for a n a l y s i s o f complex optical systems. Specif ic mathematical detai ls can be found in r e fe rences 1 3 , 17, and 18, and background treatments can be found in such t ex t - books as r e fe rences 1 9 and 20. With POLYPAGOS and similar programs, the f i r s t step i n t h e a n a l y s i s o f a system is the computat ion of the pupi l funct ion by s u i t a b l e ray-tracing procedures . The pupil func t ion describes t h e combined e f f e c t s of d i f f r a c t i o n ( s y s t e m l i m i t i n g a p e r t u r e ) a n d a b e r r a t i o n s o n the o ther - wise ideal wavefront propagated through the system.

Fourier t r ans fo rma t ion o f t he pup i l func t ion y i e lds t he ampl i tude spread funct ion (ASF), and t h e p o i n t spread func t ion (PSF) is obtained from PSF = I ASFl ’. Phys ica l ly , t he PSF is t h e d i f f r a c t i o n p a t t e r n or optical power spectrum i n t h e image p lane for a point-source object ( i n p u t ) , as would be measured with a square-law detector such as photographic film or a photo- detector. The 0°F which results from a Four ie r t ransformat ion of t h e PSF is a two-dimensional complex function t h a t may be w r i t t e n

OTF = R(fx , fy) + i I ( f x , f y )

where R and I r e p r e s e n t t h e real and imaginary parts and f, and f y are spa t i a l - f r equency va r i ab le s for t h e x- and y-directions. The OTF must be specified f o r a g iven f i e ld p o s i t i o n , f o r a g iven d i r ec t ion , and fo r a given wavelength unless a po lychromat i c quan t i ty is determined by averaging.

The phase t ransfer func t ion (PTF) is given by

1 4

APPENDIX B

and the modu la t ion t r ans fe r func t ion (MTF) by

MTF = [R2(f,,fy) + 12(fx,fyf11’2

The meanings of MTF and PTF are bes t unde r s tood by cons ide r ing t ha t a given d i s t r i b u t i o n of rad iance i n t h e o b j e c t p l a n e of an optical system can be con- s i d e r e d as a r i s i n g f r o m t h e s u p e r p o s i t i o n o f sine-wave g r a t i n g d i s t r i b u t i o n s o f rad iance of d i f f e r e n t spat ia l f requencies , phases , o r ien ta t ions , and ampl i tudes . The d i s t r i b u t i o n of i r r a d i a n c e i n t h e image can be bu i l t up f rom s inuso ids i n t h e same way. The MTF is t h e v a r i a t i o n w i t h spa t i a l frequency of t h e ratio of t h e c o n t r a s t i n t h e s i n u s o i d a l image t h a t is produced to t h e c o n t r a s t o f a s inu- s o i d a l test object.

The PTF is a measure of the l a te ra l d i sp lacemen t o f t he component s inuso ids from t h e or ig in of t h e image coordinate system; it is measured i n r a d i a n s or o t h e r a n g u l a r u n i t s , where 2n r ad ians are equ iva len t to one pe r iod o f t he image of t h e s i n u s o i d a l test ob jec t . The PTJ? is t h e l ea s t understood aspect o f t he OTF. Reference 15 (pages 33-43) shows t h a t t h e meaning of t h e PTF is always ambiguous u n l e s s t h e PSF is evenly symmetr ical . Therefore , the practical impor- t ance o f t he PTF i n image eva lua t ion is still to be fu l ly r e so lved . A l i n e a r p h a s e s h i f t j u s t t r a n s l a t e s t h e d i f f r a c t i o n image w i t h o u t d e t r i m e n t a l e f f e c t on t h e image qual i ty . Programs such as POLYPAQOS provide for automatic removal o f l i nea r phase sh i f t s . Non l inea r phase sh i f t s , however , in t roduce harmnic d i s t o r t i o n t h a t r e s u l t s i n serious d e t e r i o r a t i o n o f image q u a l i t y .

ACCOS V Camputer Program

The ACCOS V program is a comprehensive program including optimization rou- t i n e s f o r u s e in des igning and eva lua t ing a broad range of optical systems.

a process mathemat ica l ly equiva len t to the Four ie r t ransformat ion opera t ions o f t h e POLYPAQOS program. However, i f t h e f u l l two-dimensional OTF is n o t r e q u i r e d , t h e a u t o c o r r e l a t i o n process is more c o m p u t a t i o n a l l y e f f i c i e n t t h a n the Four i e r t r ans fo rm process.

. The ACCOS V program der ives the 0°F by a u t o c o r r e l a t i o n of t h e pupil func t ion ,

15

APPENDIX c

SUPPLEMENTARY MODULATION TRANSFER FUNCTION DATA

ON LIMS RADIOMETRIC SYSTEM

I n the main text of t h i s report, modulation transfer function (MTF) data were presented on the 03 and Hz0 LIMS channels over the spatial-frequency range of primary significance i n t h e LIMS application (figs. 5 and 6 ) , and the close similari t ies of data on the other channels to these two data sets were dis- cussed. I n t h i s appendix, additional M T F data for a l l s i x channels are pre- sented for spatial frequencies up to about the cutoff spatial frequency of the optical system for the C02 wavelength. The data might be of interest (perhaps aside from the LIMS application) i n the frequency response of a LIMS-type radiometric system. These results are contained i n figures C1 to C6.

I n addition to calculations of M T F a t f i e l d angles corresponding to centers of the detectors (represented by the data points i n figs. C1 to C6) , MTF' values were calculated for field angles corresponding wi th the detector extremities (see circular dots on detectors i n fig. 4 ) ; the extremity values of MTF' are represented i n figures C1 to C6 by the ends of the vertical bars. The spread (y-direction) i n M T F values for different field angles along the length (x-direction) of each detector is due to the variation i n aberrations wi th increased or decreased f ie ld angle.

The differences between the POLYPAQOS and ACCOS V MTF results may be accounted for through the considerations of the f i r s t paragraph of appendix B. However, the differences are not very significant relative to the final system M T F results (i.e., the M T F (LIMS) curves i n f i g s . 8 and 9 and f ig s . C7 to C 1 0 ) .

16

APPENDIX c

1.0

.9

.8

.7

.6

5 -5

k

-4

.3

.2

. 1

0 2

1 10

4

Center ( 0 POLYPAGOS

Extremities of

IFOV I

i. h 3 1 -

1 20

I 1 I 1 1 I 4 5 6 7 8 9 10

1

cycles/mrad 1 I I 30

1- 40 50 60

cycles/mm Spatial frequency (y- direction)

F igu re C1.- M"E'(optics) of LIMS NO2 channel.

17

APPENDIX c

1.0

.9

.8

.7

.6

Fr 2 .5

.4

.3

.2

.1

0

Extremities of

IFOV I -

-

-

-

-

-

-

-

-

I I I I I 1 1 I I I 1 2 3 4 5 6 7 8 9 10

cycles/mrad I

0 10 20 30 40 50 60 cycles/mm

Spatial frequency (y-direction)

Figure C2.- MTF(optics) of LIMS H20 channel.

18

APPENDIX c

Center 0 POLYPAGOS

Il$lV 1 0 ACCOS V

Extremities of

IFOV I

0 10 20 30 40 50 60 cycles/mm

Spatial frequency ( y-direction)

Figure C3.- MTF(optics) of LIMS 03 channel.

19

APPENDIX c

1.0

.9

-8

.7

.6

Fr 5 .5

.4

.3

.2

.1

c

‘11

I -

-

-

-

-

-

-

-

-

I I I I . ” 1 I ~ 1 0 1 2 3 4 6 7 8 9 10 5

cycles/mrad

-

1 1 I I I 0 10 20 30 40 50 60

I. L- -

Extremities of

IFOV I

cycles/mm Spatial frequency (y-direction)

Figure C4.- MTF(optics) of LIMS HNO3 channel .

20

APPENDIX c

.9

-8

.7

.6

Fr

2 .5

.4

.3

.2

.1

Center 0 POLYPAGOS IFOV Of I 0 ACCOS V

Extremities of

IFOV I

3 4 5 (

cvcles/mrad "

0 10 20 30 40 50 60 cycles/mm

Spatial frequency (y-direction)

Figure C5.- MTF(optics) of LIMS CO2(wide) channel.

21

APPENDIX C

Extremities of

IFOV I

.2 -

.1 -

I 1 I 1 . t . ." 1 cycles/mrad

I V 1" -1 1 I 0 i o 20 30 40 50 60

cycles/mm Spatial frequency &direction)

F igure C6.- MTF (optics) of LIMS C02 (narrow) channel.

22

u.uI 10

Cvcles mrad

1 ! I I l l " I I 1 I I ! I l l ! I w ~~- .

.1 1 10 Hertz

Figure C7.- Frequency response of LIMS rad iometer for NO2 channel. Dashed c u r v e i n d i c a t e s s p u r i o u s r e s o l u t i o n .

23

APPENDIX C

0

-10

-20

rn Q,

0 Q,

d

2 -30

n

-40

-50

-60

- 1

-

- .1

k - B

E

- .01

-

- .001 .01 .1 1 10

Cycles mrad

.1 1 10 Hertz

I I I l l I I I I I I I I I 1 I I I l l 1 1 1 I Cycles/km .01 .1 1 (at target)

Frequency

Figure C8.- Frequency response of LIMS radiometer f o r HN03 channel. Dashed cu rve i nd ica t e s spu r ious r e so lu t ion .

24

.. . . .... ." . . . - .. ....." 1..." , . , , .

APPENDIX C

0

-10

-20

m a,

u

I+

3 -30

a"

4 0

-50

-60 1

0 MTF(0) MTF(S)

0 MTF(F) X MTF(LIMS)

Cycles

.1 1 10 mrad

Ill "-1 I 1 1 I I 1 1 1 1 1 I LLIIII I I

LA 1111lI.. 1 1 1 1 1 I I I I 1 I ~ 1 I I I I l l I Cycles/km .o 1 .1 1 (at target)

.1 1 10 Hertz

Frequency

Figure C9.- Frequency response of LIMS radiometer for C02(wide) channel. Dashed curve ind ica tes spur ious reso lu t ion .

25

APPENDIX C

0

-10

-20

[II d a

V 3 -30

a"

-40

-50

-60

I a MTF(S)

- L Cycles mrad

-1 1 1 1 I 1 -

I I I I I l I l I I 1 I 1 1 1 1 1 L ~- 1 - 1 1-11 Cycles/km .01 .1 1 (at target)

.1 1 10 Hertz

Frequency

I

A P E N D I X D

OPTIMIZATION OF FOCAL PLANE FOR OPTICAL

TRANSFER FUNCTION CALCULATIONS

A l l the optical transfer function ( O m ) calculations on the LIMS optical system that are presented i n figures 5 and 6 and figures C1 to C6 were obtained for the best focus. The best focus is defined as the f oca1 plane for which the modulation transfer function (MTF) data for a l l the detectors are most nearly maximum for a selected spatial frequency. The spatial frequency chosen was that equal to the reciprocal of twice the detector mask width (y dimension). For the No2 and Hz0 detectors, the reference spatial frequency is 0.5 cycle/mrad, and for the other four detectors it is 1 cycle/mrad. For a given detector, t h i s spatial frequency is one-half the f i r s t cutoff i n the field-mask (slit) trans- fer function. (See f i g s . 8 and 9.)

Figure Dl shows the MTE', calculated for the reference spatial frequencies previously cited, as a function of focal position (2-direction) for a l l the detectors, as determined with the POLYPAGOS program and verified w i t h the ACCOS V program. It can be seen that the best-focus choice (zero 2 position, abscissa of f ig . Dl) is a s l i g h t compromise among the s i x detectors. However, the 20- to 30+m variation i n best focus among the s i x detectors represents only about 2 u n i t s of variation i n M T F (i .e., 2 percent of the zero-f requency value).

Figure D2 presents a further verification of the best focus choice, which is determined by using a POLYPAGOS subroutine to calculate the percentage of the radiant power from a point-source object, i n an appropriate field position, that is available at each detector (ordinate). The zero z point (abscissa) i n t h i s figure is chosen identical to that i n figure D l . The peaks on a l l these curves l i e w i t h i n 20 I.lm of the chosen best focus, and the peak M T F value for any curve is not different from the value a t z = 0 by more than 1 percent of the zero-frequency M T F value. Note that the ordinate scale i n figure D2 is expanded relative to that i n figure D l .

27

Ill I I l l1 lIllIll111l1l 1111l

APPENDIX D

1.00

.95

.go

.85

s .80

.75

.70

.65

.60

28

f = .5 cycle/mrad

0 NO2 A HN03 0 H20 fl C02(Wide)

0 O3 b C02 (Narrow)

1 I I I 1 I -20 -10 0 10 20

Variation from defined best focus, p m (2-direction)

Figure Dl .- M T F as a function of focus.

30

APPENDIX I)

100

98

96

94

92

90

aa

86

84

h

0 NO2 0 H 2 0

0 O3

I

A HN03 l l C02(Wide) b Co2(Narrow)

I I ” -80 -60 -40 -20 0 20 40

Variation from defined best focus, pm (z-direction)

F igure D2.- Detector i r r a d i a n c e as a func t ion of focus.

29

1. Gille, John C.; and House, Frederick B.: On t h e I n v e r s i o n of Limb Radiance Measurements I: Temperature and Thickness. J. A t m o s . Sci., vol. 28, no. 8, Nov. 1971, pp. 1427-1442.

2. Gille, John C.; and Bailey, Paul L.: I nve r s ion o f In f r a red Limb Emission Measurements for Temperature and Trace Gas Concent ra t ions . Invers ion Methods i n Atmospheric Remote Sounding, Adarsh Deepak , ed., NASA CP-004, 1977, pp. 195-213.

3. A b e l , I r v i n g V.: Sensors for Atmospheric Measurement. O p t . Eng., vol. 17, no. 1, Jan./Feb. 1978, p. 5.

4. Harries, J. E.: The Dis t r ibu t ion o f Water Vapor i n t h e S t r a t o s p h e r e . Rev. Geophys. & Space Phys., vol. 14, no. 4, Nov. 1976, pp. 565-575.

5. Drozewski, Richard W.; and Hatch, Marcus R.: L i m b Infrared Monitor of t h e S t r a t o s p h e r e (LIMS) Experiment. Opt. Eng., vol. 17, no. 1 , Jan./Feb. 1978, pp. 14-22.

6. Bates, J e r r y C.; Hanson, David S.; House, Fred B.; Carpenter, Robert O'B.; and Gille, John C.: The Syn thes i s of 1 5 ~ Infrared Horizon Radiance Pro- f i l e s Frm Meteorological Data Inputs . NASA CR-724, 1967.

7. Thomas, John R.; Jones, Ennis E.; Carpenter , Robert O'B.; and Ohring, George: The Analysis of 151-r Inf ra red Hor izon Radiance Prof i le Var ia t ions Over a Range of Meteorological, Geographical, and Seasonal Conditions. NASA CR-725, 1967.

8. Williamson, W. R.; Shafer, D. R.; and Dilworth, D. C.: Lower Atmosphere Canposit ion and Temperature Experiment. O p t . Eng., vol. 13, no. 4, July/Aug. 1974, pp. 303-306.

9. Drozewski, R. W.; Gille, J. C.; Thomas, J. R.; Twohig, K. J.; and Boyle, R. R.: Limb Radiance Inversion Radiometer. NASA CR-143712, 1975.

10. Otnes, Robert K.; and Enochson, Loren: D i g i t a l Time Ser ies Analys is . John Wiley & Sons, c.1972.

1 1 . Bendat , Ju l ius S.; and Piersol, Allan G.: Random Data: Analysis and Measurement Procedures. John Wiley & Sons, Inc., c.1971.

12. Norton, Clarice L.; B r o c k , Gerald C.; and Welch, Roy: Optical and Modulat ion Transfer Funct ions. Photogram. Eng. & Remte Sensing, vo l . X L I I I , no. 5, May 1977, pp. 613-636.

13. Brewer, S i l a s : POLYPAGOS: Polychromic Program for the Analys is of General Optical Systems. SAMSO-TR-70-411, U.S. A i r Force, Sept. 1970. (Available from DM3 as AD 71 5 262. )

30

15. Image Assessment SI Specification. Volume 46 of Proceedings of Society of Photo-Optical Instrumentation Engineers, David Dutton, ed., c.1974.

16. Specification and Evaluation of Optical Systems. Opt. Acta, vol. 22, no. 4, Apr, 1975, pp. 242-390.

18. Parsons, John R.: Sampling Functions and Their Effect in Optical Systems Evaluation. SAMSO-TR-71-78, U.S. Air Force, Dec. 1970. (Available from DDC as AD 724 626.)

19. Goodman, Joseph W.: Introduction to Fourier Optics. McGraw-Hill Book Co., Inc., c. 1968.

20. Gaskill, Jack D.: Linear Systems, Fourier Transforms, and Optics. John Wiley ti Sons, c. 1978.

31

LIMS channel

(species)

NO2

N20

03

H*3

C02 (wide)

C02 (narrow)

TABLE I .- LIMS MEASURED FREQUENCY RESPONSE

P ~~

Square-wave response a t frequency, cycles/mrad, of - 0

1 .o

1 .o

1 . o

1 .o

1 .o

1 .o

". . - _~

__

0.1

1 . l o o

1.079

.992

1.035

1.007

1.031

0.2

1.047

1.064

1.039

1 .079

1.017

1.038 _- ~ "

0.4

0.694

.728

,926

.962

.930

.958

0.6

0.18

.20

.771

.758

.739

.742

0.7

""_ ""_ 0.682

.651

.638

.623

___

0.8

""_ ""- 0.580

.524

.541

.505

1 .o "_" ""- 0.338

.295

.304

.282

1.2

""_ ""- 0.1 59

.122

,149

.122 II__-

32

1 .o

.8

.6

.4

.2

0 8 16 24 32 40 48 56 64

Altitude, km

Figure 1.- Model radiance profiles of atmospheric constituent gases.

w w

loo

10-1

a,

10 -4

Spatial frequency, cycles/km

Figure 2.- Fourier input spectra for LIMS model radiance profiles.

34

I r t ran 6 (CdTe) window (152 K) lT7 Thermal mask (152 K)

I r t ran 6 lens

Secondary arabolic mi r ro r (Au -\ li Folding mi r ro r (Au)

A Primary parabolic Scan mir ror (Au) mir ro r (Au)

\ \ \ Limb

radiation Note: Unless otherwise

indicated, components are at 297.5 K

Figure 3.- LIMS optical schematic.

I O3 X = 9.64

2 k d 4 \, HNOQ X = 11.32 p m

4.1 mrad (.6425 mm) - 5 " C02(Wide) h = 15.20 p m

(.785mm) 6.65 mrad 1 C02(Narrow) X = 15.23 p m .5 mrad (.079 mm) (1.042 mm)

b- 8 mrad (1.254 mm)

36

1.0

.9

.8

.7

.6

.4

.3

.2

.1

0 0.5 1 .o 1.5 2.0 2.5 3.0 3.5 4.0 cycles/mrad,

5 10 15 cycles/mm

Spatial frequency

20 25

Figure 5.- MTF (optics) of LIMS 03 channel.

37

1.0

.9

.8

. 7

.6

Fr g .5

.4

.3

.2

.1

0 0.5 1 .o 1.5 2.0 2.5 3.0 3.5 4.0 cycles/mraI

I I I I 0 5 10 1 5 20 25

cycles/mm Spatial frequency

Figure 6.- MTF(optics) of LIMS H 2 0 channel.

N02

- n/12 O L - ~

r - n/12 O L

H2°

- n/12 O L -

HN03

C 0 2 (Wide)

O b -

-n/12 I~ -1- 1 1 1 1 1 1 !"A 0 1 2 3 4 5 6 7 8 9 10

Spatial frequency, cycles/mrad

F igure 7.- Phase t r ans fe r func t ion (P'IT) of LIMS optics.

39

0

-10

-20

rn a,

0

d

2 -30

a"

-40

-50

-60

1

.1

Fr - b E

-*01 t r

- .001 I I I L L 1 1 1 1 i 1 I l L .01 .1 1

Cycles 10 mrad

Frequency

Figure 8.- Frequency response of LIMS radiometer for 03 channel. (Desired pass band is 0.0 to 0.2 cycle/km. ) Dashed curve indicates spurious resolution.

40

0

> -10

-20

l-4 v1

; -30 a" 0

-49

-50

-60

- 1

-

- .1

crr -I3 E

- .01

L

-.001 Cycles .01 .1 1 10 mrad

1 - 1 1111 - I I 1 1 1 1 1 1 1 I I I 1 I I I I I 1 .1 1 10 Hertz

U U L I I 1-1 I l 1 I I l I 1 I I I I I I I 1 Cycles/km .01 .1 1 (at target)

Frequency

Figure 9.- Frequency response of LIMS rad iometer for H20 channel . (Desired pass band is 0.0 to 0.1 cycle/km. 1 Dashed curve i n d i c a t e s s p u r i o u s r e s o l u t i o n .

41

10'

10 -I

F4 5

IO -3

IO -4 L 10-I

Frequency, Hz

dh _J

l o2

Figure 10.- Fundamental and f i r s t side band of sampling response. (Desired pass is 0.0 to 0.2 cycle/km. )

42

.01 .1 1 I 1 I l l 1 I l l I I 1 I 1 1 1 1 1

10 100 Spatial Frequency, cycles/mrad

Figure 1 1 .- Phase t rans fer funct ion of LIMS radiometer.

43

r ”””””” 1

”-

Figure 12.- ElTF test configuration.

44

3 800

3 400

3000

2 600

+ s a c,

g

g

v

v)

r=

u

2200 -w

1800

1400

1000

600 1 2 3 4 5 6

Time, sec

(a) Target segment 1.

Figure 13.- L I S output of MTF test.

45

3 800

3 400

3000

2600

h + 2 .w - 2200 4 (II

E: 5 0 u

1800

1400

1000

600 2

L 3

r

I

4

i

Time, sec

(b) Target segment 3.

Figure 1 3. - Continued.

46

3 800

3 400

3000

2600

h - 4 2

5 s 0

4 rn G

- 2200

u

1800

1400

1000

600 1 I 1 2

I 3

Time, sec

1- 4 5 6

(c) Target segment 5.

Figure 13 . - Concluded.

47

0

-10

-20

r/l a,

u

4

2 -30

a"

-40

- 50

-60

1(

.1

R - b E

- .01

- .001

LIMS MTF response

LIMS square-wave response

"-

0 Measurements on flight sensor, from square- wave input

, I , , , , I Cycles 10 mrad

Hertz .1 1 10

- 1 1 I I I I I I I I 1 . 1 I I I I I I Cycles

.01 .1 1 km (at target) Frequency

Figure 14.- Frequency response of LIMS radiometer for 03 channel.

4a

. "

Spatial frequency, cycles/km

Figure 15.- Prediction of LIMS spectral output. Dashed line indicates extrapolation of data.

49

I 11111 .

1. Report No.

NASA TP-1504 4. Title and Subtitle

SPATIAL-FREQUE3

I ..

2. Government Accession No.

NCY RESPONSE OF THE LIMB INFRARED MONITOR OF THE STRATOSPHERE

7. Authorb)

R. Gale Wilson, Anthony Jalink, Jr., and William M. KahlFum, Jr..~

9. Performing Organization Name and Address . . . . . .~ ..

NASA Langley Research Center Hampton, VA 23665

12. Sponsoring Agency Name and Address -~ -

National Aeronautics and Space Administration Washington, DC 20546

15. Supplementary Notes ..

16. Abstract

3. Recipient's C a t a l o g No.

5. Report Date August 1979

6. Performing Organization Code ~~

- 8. Performing Organization Report No.

L-13037 10. Work Unit No.

642-1 2-1 1-01 1 1 . Contract or Grant No.

13. Type of Report and Period Covered

Technical Paper ~ .~

14. Sponsoring Agency Code

The Limb Infrared Monitor of the Stratosphere (LIMS) is one of the experiments on the Nimbus-7 s a t e l l i t e . I t is designed to scan the Earth's l imb ver t ical ly and to measure spectral emission profiles of trace atmospheric gases that are believed to be important i n processes controlling the stratospheric ozone distribution. The LIMS mus t have adequate spatial-frequency response for a l l the spectral channels to provide, through inversion of the measured limb radiance profiles, important information about the temperature, structure, and composition of the atmsphere. Experiment objectives are reviewed and several analyses and measurements are described which were performed to determine the adequacy of the system for satis- fying these objectives. From the LIMS design-model data, the modulation transfer function (MTF) was calculated for the optical system, the detector field mask, the electronics, and the overall system for each channel. The signal output per- formance of the instrument was predicted from the system M* data and model input radiance data for each channel. The MTF measurements made on the flight sensor confirmed the analytical results. The predictions indicate that the instrument can sa t i s fy the basic measurement objectives of the experiment.

7. Key Words (Suggested by Authorb))

Infrared Stratosphere Air pollution Limb Atmosphere Spatial-frequency response

18. Distribution Statement

Unclassified - Unlimited

Subject Category 45 . . ~

19. Security Classif. (of this report) 20. Security Classif. (of this page) 1 21. No.4; 7 22. Price'

Unclassified $4.50 - -~ Unclassified

* For sale by the Nat lonal Technical Informat ion Service. Spr inEfreld. Vlrginla 22161 NASA-Langley, 1979

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