N O T I C E 

THIS DOCUMENT HAS BEEN REPRODUCED FROM 

MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT 

CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED 

IN THE INTEREST OF MAKING AVAILABLE AS MUCH 

INFORMATION AS POSSIBLE 
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. JPL PUBLICATION 79-109 . 

Application of Digital Image 

Processing Techniques to 

Astronomical Imagery 19.79 

Jean J. Lorre 

(11SA-CR-162811) lPPLICA1IOH OF DIGITAL N60-19996 

II1GE PROCESSING TECBIIQUES TO ASTROIOftICAl 

IIIG!RY, 1919 (Jet Propulsion Lab., 15 p 

HC 10'l/!F A01 CSCL 03A Dnclas 

November 1, 1979 

National Aeronautics and 

Space Administration 

Jet Propulsion Laboratory. 

California Institute of Technology 

Pasadena, California 

G3/89 41585 

\ 
· .. 

fU tt 

JPL PUBLICATION 79-109 

Application of Digital Image 

Processing Techniques to 

Astronomical Imagery 1979 

Jean J.lorre 

,,"aem ... • oa iLL.iliAlI. 

November 1, 1979 

National Aeronautics and 

Space Administration 

Jet Propulsion Laboratory 

California Institute of Technology 

Pasadena, California 
PREFACE 

The work described in this report was performed by the Observational 

Systems Division of the Jet Propulsion Laboratory. 

AC KNOW LEDGMENTS 

The activities described in this report were encouraged by Dr. Nancy 

Roman, Dr. Jeffrey Rosendahl, and Or. ~ward weiler at NASA Headquarters. 

William B. Green, Manager of the Science Data Analysis Section which includes the JPL Image Prooessing Laboratory, was instrumental in supporting 

this project. I wish to thank Dr. Stephen Gull of Cavendish Laboratories 

for his algorithm implementing the Maximum Entropy concept; Drs. Halton 

Arp and Jack Sulentic of Hale Observatories for their suggestions and 

plates of M87; Or. Allan Sandage of Hale Observatories fer his suggestions 

and plates of M82; and Peter Kupferman of JPL for his relentless efforts 

to reduce the silicon vidicon images of planetary nebulae and to master 

VICAR. 

PRECEDING PAG£ BLANK NOt fiLMED 

iii 

-os 1m Mt"g rt 

Ie 
ABSTRACT 

Several areas of applioations of image prOcessing to astronomy 

have been identified and developed in this report. These areas include: 

1. 

Deconvolution for atmOSPheric seeing oompensation; a oomparison 

between maximum entropy and conventional Wiener algorithms. 

2. Polarization in galaxies from Photographic plates. 

3. Time changes in MBT and methods of displaYing these changes. 

~. Comparing emiSSion line images 1n Planetary nebulae. 

5. Log Intensity, Hue Saturation Intensity, and Principal Component color enhancements of M82. 

6. Decallbration of CCD arrays for spatial sensitiVity variations. 

Objeots. Examples are presented of these techniques applied to a variety of 

iv 

'tt m '"sW'_ !'S 1 it; i f# 
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CONTt;NTS 

I. INTRODUCTION ------.-------------------------.--------------- 1-1 

11. DECONVOLUTION - MAXIMUM ENTROPY VS. WIENER ------------------ 2-1 

111. POLARIZATION IN GALAXIES ------------------------------------ 3-' 

IV. TIM~ CHANGES IN M81 ----------------------------------------- ~-1 

V. PLANETARY NEBULAE - COMPARING EMISSION LINE IMAGES ---------- 5-1 

VI. COLOR ~NHANCEM~NTS ------------------------------------------ 6-1 

A. LOG INTENSITY STRETCH ----------------------------------- 6-1 

B. HSI ----------------------------------------------------- 6-3 

C. PRINCIPAL COMPON~NT ______________________________ w __ .___ 6-5 

VII. DECALIBRATION OF ceD ARRAYS --------------------------------- 7-1 

VIII. SUMMARY AND CONCLUSIONS ------------------------------------- 8-1 

R~FeHENCES -------------------------------------------------- 9-1 

Figyres 

1. ~t..lximum entropy VB. Wiener restoration on a noiseless 

blurred target ---------------------------------------------- 2-3 

2. Maximum entropy vs. Wiener restoration on a blurred 

target with an RMS = 30 noise level added ------------------- ~-4 

Maximum entropy vs. ~iener restoration on a blurred 

target with an RMS = 60 noise level added ------------------- 2-5 

4. Maximum entropy vs. Wiener restorati0n on a blurred 

noiseless target -------------------------------------------- 2-6 

5. "j.ximum entropy vs. Wiener restoration on a real 

scene of Mb7. Bottom row are each Wiener restorations 

with signal-to-noise ratios of 4, 8, and 1~ ----------------- 2-7 

6. Maximum entr'opy VB. wiener restoration on a real 

scene of M87 -.---------------------------------------------- 2-8 

7. Maximum entropy restoration of blurred decimated 

images ------------------------------------------------------ 2-9 

v 

Sf'.';: • • ."! be . r-:tpi~ -
8. Maxlmum entropy va. Wiener restoratlona for onedi.ensional spectra --------------------.-.------------------ 2-10 

9. Maximum entropy va. Wiener reatoration for an RMS noiae 

of 2 added to the dearaded 1meae ---------------------------- 2-" 

10. Maxlmum entropy va. Wlener restoration for an RMS 

noise of 6 added to the dearadad imeae ---------------------- 2-12 

11. H82 dlfference im~e 1n the aenae E-vector alona the 

major axla minus I-vector normal to the major axis ---------- 3-3 

12. M82 polarization image scaled with 25 percent 

polarization to white --------------------------------------- 3-~ 

'3. H82 polarization image In the aame format as 

F1&ure 12, but computed from smoothed Imaaes ---------------- 3-5 

,_. H87 mosaio diaplayina four polarization orientations, 

each in 6- and 3-m1nute expoaures and each at two 

epocha, 1956 and 1978 --------------------------------------- ~-2 

15. M87 differenoe imagea 1n the senae 1978 minus 1956, 

eaoh In four polarization orientat10na ---------------------- 4-3 

16. M87 difference imaaes 1n the same format as F1&ure 15 ------- 4-4 

17. NGC6720 mosaio of nine emission line images after 

radiometrio oorrection and soalina for visual 

interpretation ---------------------------------------------- 5··4 

18. NGC6720 two-dimensional Fourier transforms displ~yed 

as log amplitude in a one-to-one oorrespondenoe with 

the images of Figure 11 -------------.----------------------- 5-5 

19. NGC6720 mosaic of modified transforms in the same 

rormat as Figure 18 --.--------------------.----------------- 5-6 

zo. NGC6720 mosaic 1n tbe same format as Figure 17 after 

tbe reduction of all noise souroes -------------------------- 5-7 

2'. NGC6720 mosaic of polar coordinate transformations 

in the same order as Figure 20 ------------------------------ 5-8 

22. NGC6720 mosaic of the volume emission coefficient 

at different wavelenaths suitably scaled for viewing -------- 5-9 

23. NGC6720 temperature map scaled for viewing ------------------ 5-10 

24. NGC6120 electron density map scaled for viewing ------------- 5-1' 

25. NGC6720 mosaic of different images oolor coded green 

and added to the Hn imaae coded red ------------------------- 5-12 

vi 

.......... 
t 

I 

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26. NOC6720 color-coded rendition of ionization struoture. 

Color assignments are blue cHell, 4686; green = Hel, 5876; 

J~ed : (01), 6300 -------------------------------------------- 5-13 

21. NGC6720 color-ooded rendition of ionization structure. Col~r 

assignments are blue = [OllJ, 3721; green: (0111), 5007; 

red: (01), 6300 --------------~----------------------------- 5-14 

28. M82 mosaic of four combinations of three colors eaoh -------- 6-8 

29. M82 mr'saic after the LOI Intensity transformation which 

preserves but does not enhance oolor differences ------------ 6-9 

30. M82 mosaic after Log Intensity transformation but coded 

witt 101 intensity 1n equal reflectance steps --------------- 6-10 

j1. M82 mosaic of the four individual oolors after the LOI 

Intensity transformation ------------------------------------ 6-11 

32. M82 mosaic of three struotural bands ------------------------ 6-12 

33. M82 mosaio 1n the same format as Figure 32. From the top 

down, the left column pictures are 103aO, lu3aD, and Hu ----- 6-13 

34. M82 mosaic 1n the same'format as Filure 32. From the top 

down, tile left column pictures are 103aO, 103aE, and lia ----- 6-14 

35. M82 mosaic in the same format as Figure 32. From the top 

down, the left column pictures are 103aD, 103aE, and Hn 6-15 

36. M82 mosaic after HSI oolor enhanoement with the hue, 

satuation, and intenSity transformation and coded with 

log intenSity in equal density steps .----------------------- 6-16 

37. M82 mosaic after HSI color enhanoement the same as 

Figure 36, except with log intenSity coded into equal 

reflectance steps ------------------------------------------- 6-17 

38. i-182 mosaic of pure hue after discardinl the saturation 

and intensity images in the HSI transformat·ion -------------- 6-18 

39. M82 mosaio of the principal component images produced 

from four spectral bands ------------------------------------ 6-19 

40. M82 mosaic of color-enhanced reconstructions from the 

prinCipal component images of Figure 39 --------------------- 6-20 

41. M82 mosaic of color-enhanced images produced the same 

way as Figure 40, but with an intermediate filter which 

smoothed in inverse proportion to the information content 

of each prinCipal component band ---------------------------- 6-21 

42. Scaled display of the response of a CGD array to a flat 

field ~t1mulus ---------------------------------------------- 7-3 

vii 

-~1 

1 ; 

, 
43. Scaled display of the multiplicative term of the 

oallbration f11e used to decalibrate the CCD 1m .. e of 

Fiaure 42 -------------------------.------------------------- 7--

44. Scaled d1splay of the offset term of the oalibration file 

used to decalibrate the CCD imase of FIlure 42 -------------- 7-5 

45. Soaled deoalibrated CCD flat field image -------------------- 7-6 

46. Variance imase displaying the variances of each pixel in 

a set of five ident.1cal exposures in an undeoal1brated 

field ------------------------------------------------------- 7-7 

Tables 

1. Wavelengths of Each Planetary Nebula Image ------------------ 5-1 

2. Color Assignments of Narrow Band Images for Filures 26 

and 27 ------------------------------------------------------ 5-3 

3. Standard Color Assignments for the M82 Hosaics -------------- 6-2 

4. &Dulsion/Filter Combinations -------------------------------- 6-2 

5. Assignments of Bands to Primaries in Figures 32 through 35 6-4 

6. Information Content in Each Principal Component Image 

of M82 for Figure 39 ---------------, .. ------------------------ 6-6 

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SECTION 1 

INTRODUCTION 

Astronomy has traditionally made great use of imasery, but this 

data has almost exolusively been evaluated via the photographio prooess. 

With the advent of the unmanned planetary mia.ionD and digital oameras, 

teohniques for prooessing digital images have been developed and are 

beginning to be applied in astronomy. The advantases of digital imases 

over photographio ones are very great and, with the development of new 

algorithms and oameras, beoome greater all the time. It is thus of importanoe to searoh for applioations and disseminate digital teohniques 

to the astronomical oommunity at large. When Spaoe Telescope becomes 

operational, the quantity and unprecedented quality of the oalibrated 

digital images returned will oall for every available processing means 

at our disposal. This report is intended t~ provide a few of those 

!:leans. 

This work was performed during 1979 at the Image Processing Laboratory (IPL) of JPL under FY79 RTOP '389-~1-01. It represents a continuin~ 

effort (References 1 and 2) to identify and develop new image procesei~& 

applioations to astronomy. Additional goals of this researoh are the 

further education of the astronomical community in digital image processing 

techniques and the expansion of methods tor analysis of high-quality space 

telescope imagery when it becomes available. Hopefully, others will be 

inspired to find applioations to their own diSCiplines. 

This report is divided into eight sections. Sections II through VII 

present techniques applied to a major topio. The data used and the techniques involved are described in detail, along with photographs and plots 

o( the results. Section VIII gives conclusions that can be made as a 

result of this work. This report illustrates image processir~ and does 

not interpret the physioal significance of results that develop from the 

data. The role ot data interpretation resides with the collaborating 

astronomer. Image processing is a vehicle to strengthen and simplify 

his task. 

1-1 
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SECTION II 

DECONVOLUTION - MAXIMUM ENTROPY VS. WIENSR 

The Ilcorithm d.veloped by Dr. Gull and Dr. Dani.ll (R.ferenoes 

3 and ~) tor oorr.otins inoomple~e radio map. wa. provided in a torm 

suitable tor deoonvolution ot optical ta .. es (R.ference 5). Th1. teohnique has prov.n very succ.saful 1n re.tor1ns Fourier transrorms, and 

the philosophy is applioable to solvina. in an it.rat1v. tash10n. the 

,.neral 1nv.r .. problem. 

The maximum entropy teohnique hal leveral desirable properties 

whioh are not observed by lin.ar filters: 

(1) It produce. a unique map. 

(2) The restored intenSity values are non-nesativ •• 

(3) Rinaina (Gibbs phenom.na) ls virtually und.tectable. 

To provide a oontrol, an a-bit synth.tic imas' was cr.at.d (upp.r 

left corn.r of Fl,ur, 1). This 1m ... was convolved with a 5-by-5 el •• nt 

kernel of equal weight whioh replaced each pix.l by th. m.ans ot its 

n'lIhborhood (upper r1&ht of Fi,ure 1). lb. object was to r"tor. 

the de,raded imas' to its orl,1nal form. In the central row of F1&ur. 1, 

the left imlle represents the maximum entropy restoration and the r1&ht 

imag. repr.sents the wlener lin.ar restoration (Referenoes 6 and 7). 

The lowr l.ft tall' of' Figur. 1 contains the chi squared residuals 

.ap of the maximum .ntropy restoration, i ••• , the ratio of mi.tit to 

the data to the error due to noise in the data. Th. lower r1&ht imlle 

ot Fiaure 1 contain. the loa HTF or the kernel used to d.grade the 

oriainal. i.e., the log modulus of the Fourier transform ot the 5-by-5 

element point spread funotlon. TI~. particular kernel is not trivial 

to correot tor because it Introd~ s both 1800 phase sh1rt. and croaae. 

the z.ro amplitude plan. (dark bars) 1n many plao.s. 

In the oaae illustrated by Figur. 1 (whioh is nol •• 1e81 it on. 

can dlsre,ard the RMS int.ger trunoation noise of , 12/3 ) t th. Wi.ner 

model, ev.n wlth • mod'st li,nal-to-noi.e ratio or 15. i. more .ft.ctiv. 

for visual recognition. 

fi,ures 2 and 3 demonstrate the effect of adding random noise 

to the dearaded imag' before restorat1on in RMS quantities ot 30 and 

60. respectively. In Figure 3. the true sianal-to-noi.e ratio in the 

1mage 1s apprOXimately unity and the linear model has been toreed to 

further blur the data 1n order to improve it. The two allor1thms operate 

with equal erreotivenes. in Figure 2. In Fllure 3. the nOise level is 

almost too high ror either algorithm to errect an improvement. 

In Figure 4, a larger tilter or 9-bY-9 elements has been employed. whioh haa destroyed the control beyond the human pattern recognition 

oapability to recocnlze any character.. No noiae was added and the 

linear model was able to restore most or the image into the reoocnizable 

range. 

2-1 

I~~··~· ~ ____ ~m.'~r""nO~ __ ~'w •• ·~1 ... ~_:.1fr~~--...... ~.~-•.. ;r;;~ii~.c .. ai5;ei;.i";.j.~==~==~~ .. ~.~.[~ ........ -- ~ 
It appears from the above exercise that the lIlaxian.lll ent.ropy restoration is able to compensate for AaU amounts of blurrina in the prea.it':--=' 

of nOise and to produce relatively artitact-tree 1m ... s when the nOis. 

level is mod.rate. Th. Wi.ner 1Il0del 1s superior trom a subjective 

standpoint only in the low-noise regille. 

To compare both alaorithllla on aatronomical 111l88ea, tour platea 

taken throuah a polaroid at PfA. 2_50 ot H87 were Iverased. Reference 

atara were selected trom the tield and placed into a row at the bottom 

of the iml&e. Theae stara provided the required point spread function. 

Figure 5 illustrates a lIlosaic of .everal illl&8es of H87. On the top 

row the left imase is the oriainal, the mijdle is the maximum entropy 

restored version, and the riaht illl&8e il the chi squared residuals 

map. On the bottom row from lett to riaht are linear Wiener model 

restorations with sianal-to-noiae values of ~, 8, and 1_. The lIlaximum 

entropy restoration is Virtually artifact free but is only sliahtly 

enhanced. The Wiener restorattons. although full of artifacts, provide 

better restoration where the ai,nal-to-noise ratio is hiah. The background artifact is due to the linear model's assumption that the 

slgnal-to-noise ratiO is independent of position. It is ironic that 

the chi squared residuals map is .s interestins as the restoration. 

In Figure 6, a similar picture to Fi,ure 5 is presented, which provides 

a better maximum ~ntropy restoration. This was accomplished by smoothins 

the orisinal imase with a amall convolutional filter, thus improving 

the on,'iu.l Itianal-to-noise ratio by suppreasins the hiaheat frequencies. 

It is important to consider that, because the maximum entropy 

technique produces little artifact, it may be more valuable tn employ 

in cases where the true nature ot the object cannot be estimated beforehand. 

One of the powerful capabilities of the maximum entropy restoration 

is its ability to assign noise wei~htina to the 1mage on a pixel-to-pixel 

basia. As an example of this, the control imase used in Figure 1 was 

degraded with a 7-by-7 kernel and then decimated with a random grid (ahown 

at the bottaa left of Figure 7). The lower riaht of Flgur'e 7 shows 

the restoration. Althoush this restoration is not better than the blurred 

version, the application of any linear convolutional model would have 

reaulted in a totally unrecognizable picture. 

A compariaon of both alaorithllls was also performed upon synthetic 

spectra in order to evalute their performance in one dimension. Each 

of the three figures, Fiaures 8, 9, and 10, containa the original apectrum 

at the top, the degraded and noiae added spectrum at the bottom and, 

in the aecond and third rows from the top, the maximum entropy and Wiener 

model restorationa respectively. The object was, as usual, to reconstruct 

the top row from the bottom one. Fiaurea 8, 9, and 10 differ insofar 

as the ~ nohe added to the degraded spectrWII was zero for Figure 8; 

two for Figure 9; and aix for Figure 10; with corresponding Wiener 

signal-to-noise values of 20, 10, and~. From a comparison of Figures 8, 

9, and 10, it can be seen that once again aa in the case of the twodimensional restorations the linear model is superior when the noise 

level is very low. At intermediate noise levels, the two algorithms 

are very similar, and, at hiah noile levela, they become equally unreliable, prodUCing artifacts. 
I 

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Figure ,. Maximum entropy vs. Wie~ " re'toration on a noiseless blurred 

target: (top left) ori b .r.al; (top right) blurred target; 

(center left) maximum entropy restoration ; (center right) 

Wiener restoration; (lower left) maximum entropy chi squared 

residuals; (lower right) transfer function of the degrading 

filt r, a 5-by-5 lement box filt r. 1he Wi ener signal-to-n0ise rat!o was '5. 

2- 3 
Figure 2. Maximum entropy vs. Wiener re storation on a blurred tare t 

with an RMS = 30 noise level ~dded. The wi ene r ~igna - t o- '1ois 

ratio was 5. 

2- 4 
Figure 3. Maximum entropy vs. Wiener restoration on a blurred target 

with an RMS = 60 noise level added. The wiener 

signal-to-noise ratio was 2.5. 

2-5 
Fi'UI" 4, MaximwlI ' ll tl' py , Wil'IlL'I' 1't:'s t OI',l t ioll 011 ,1 blU!'I".! lloiSCit'ss 

t.ll'get, Th e degl';Id i ll' t'iltL'I' was ill'!'I',L1t'd ill 31..1' ll-by_ll 

l c:n 'n t s , 

'-0 
Figure 5. t-1a ximum ent r opy vs . wiener restoration on a real scene of 

I'1 d7 : \ top l eft) original; (top middle) maximum entropy 

r e stJration ; (top ri g ht) ch i sq uar ed r esidual s . BotL ~ 

row r e ac h hiener r estor at ion s with signal- to- noise r at i os 

fr om l eft to right of 4, H, and 14. 

2- 7 

r , 7r' 
Figure 6 . Maximum entropy vs. wiener restoratlon on i\ real scene of 

M81: (top left) smoothed original; (middle) maximum en ropy 

restoration ; (righ ) chi squar d residuals. 

2- 8 
Figur 7. M 

( 

d cim 

ion of 

) orig inal ; ( op righ 

imag ; (low r !'igh ) 

d im g s : 

; (low r 1 f ) 
I/" 

lI! 

II 

II 

! I 

i I 

i i 

r 1\ II 

! , 

: I 

! I 

Ii 

~ 

'l/\I!v/lh\ l.r\l1F~ rfvv~rl/If~ (l\rv'W .rAvA~ (VV 1 if! ~ \ V ~ \ 

I 

I 

i 

i I 

~\~ij(\j'V\J 

W 

Figure 8. Maximum entropy va. Wiener restorations for one-dimensional 

spectra: (top) original spectrum; (bottom) noiseless degraded 

spectrum; (second row) maximum entropy restoration; (third 

row) Wiener restoration with a signal-to-noise ratio of 20. 

2-10 

--_IE,. .-"
~-I 

Figure 9. Maximum entropy vs. Wiener restoration for an RHS noise of 

2 added to the degraded image. The Wiener signal-to-noise ratio used was 10. 

2-11 
j nul r. r. ~I'-" r\~ \ ~rv-\ f\ ' ..... A

I r\/,\ n n (In\l~ n ~ fI rJt1 ~ '1"\ } f ," ~:! \,I/~ .. :II L \ .. 1; 1\ l'.i.'Y 'L I V 1\1~ ~ V\I'\! li~~ V1r\r~ \ Iii l( I; : I I I I i 1 ~ \ I I l : I U \ I L 

L, I.: ~ ~ : \~ I ; l! V' '\ r III 

':', I" I :! V : I 

'. " 

.. 

. . 

, , , 

, I , . 

Figure 10. Maximum entropy vs. Wiener restoration for an RMS noise 

of 6 added to the degraded image. The Wiener signal-to-noise 

ratio used was 4. 

2-12 

.. _ ~_~~" __ ~~ _ ltt we ti *«H 
SECTION III 

POLARIZATION IN GALAXIES 

'_'_~W~"'.-'C''''''''~' ,."". . .. --I .... 

, ,.. - .t 

,~ 

. l 

l 

Plates of M82 obtained by Dr. Allan sandage of Hale Cbservatories 

in two polarization orientations were soaled such that the mean sky 

level was centered at zero and the variance. of both images were identical • .. Even though only two E.vector orientationa were known. it wa. possible 

to compute the polarIzation beoaus. the direction of the polarization 

vector was known to be approximately tangential about the center of 

the M82 nuoleus (Referenoe 8). 

F1sure 11 illustrates the difference between two images in the 

sense i-vector along major axis minus E-vector along minor axis. M.lch 

filamentary structure is visible, all due to polarization. For the 

case of' foW" I-vector posi U<ina Jf5° apart. the polarization oan be 

computed trom Equations 1 through 4. 

Q 100 - 1900 

- = I 100 + 1900 

U 1450 - 1'35° -. I 1450 + 1'350 

U 

tan 29 :: -

Q 

Relations (Eq. 1-~) oan be combined to give 

~ tan 29 

u 

= -I 

and trom this and relation (Eq. 4) 

P = ~ V '+ tan2 29 

3-1 

= t 

{n 

(2) 

(4 ) 

(5 ) 

(6 ) 
the form when the angle is known. The tan2 20 acts as a modulating term 

which corrects for the polarization amplitude at other that 0 and 90 

degrees. At multiples of 900 beginning at 450 , the function becomes 

unstable and results in noise amplification, leaving a cross in the 

polarization picture. Figures 12 and 13 illustrate the polarization 

map of M82 both before and after local smoothing of the original images. 

In both cases 25 percent polarization is equivalent to white, and zero 

is equivalent to black. Because of the low signal-to-noise ratiO near 

the plate background, low-intensity values become corrupted by noise 

and result in spuriously high polarization values giving rise to the 

white ring around M82. A threshold was applied to the algorithm which 

set t.he polarization to zero if the intensity in either frame fell below 

a certain level. This gave rise to the dark region outside the bright 

noise-induced halo. Due to assumptions made in scaling the images, 

the polarization on the bar of the galaxy is constrained to be zero. 

The filaments, which extend normal to the bar, are highly polarized 

at about 20 percent. 

from inspection of the previous formula, it is clear that noise 

will severely influence the measure of polarization if either: 

(1) The differences between intensities are on the same order 

as the RMS noise. 

(2) The intensities are so low that their sums are on the same 

order as the RMS noise. 

3-2 
Fi g ure ", M82 differ enc image in the sense E-vector along the major 

axis min u :'-ve" tor normal to the major axis 
fi ur 12 . 

j -
F i 

u. 1. M po 10n 1m 

fOI':n 

s ri ur " 

u 
SECTION IV 

TIME CHANGES IN M87 

Plat •• ot M87 v.r. tak.n in two .pooh., on. 1n 1956 by Dr. Baad. 

and the other in 1978 by Dr •• Arp and Sul.ntlo ot Hale Ob •• rvatori ••• 

Eaoh Nt ot plat •• was recorded at 3- and 6-ainute apo.ur •• and .aoh 

at tour polarization ori.ntation.. A .o •• io ot all 8ixt.en t. .... i. pr ••• nted in F1Iur. 1Ji. Eaoh t. ... was .ubjected to an .pproxlaat. 

HD oorrection by toroina the .tlllar pro til •• to be Gau •• ian, th.r. 

b.inc no oth.r oalibration av.Uabl.. Eaoh ot the 1IIac" was th.n 

rlli.t.red u'i", torllround .tar., and .evlral r.t.r.nol .t.r. v.r. 

oollected into a row b.low the oorr •• pondinc t. ... ot M87. 

In ord.r to ob •• rv. any rll.tiv. int.n.ity v.riation. with tia. 

in the knot. alona the aaln j.t, the t. .... wer. nonaallz.d .uoh that 

the o.ntral ,alaxy and it. halo v.r. ot tM .... upUtud.. A .1allar 

.naly.i. but nona&1izinc the r.t.r.no •• tar. to the ...... plitud. 

vu pertonald and i. in pr ••• (R.t.r.no. 9). Att.r nonaa11li"l the 

halo, ditt.rlnol piotur •• in the .. n •• ot 1978 ooapared to 1956 v.r. 

,.n.rai.1d and art pr •• ented u F1Iur •• 15 and 16i FlIur. 15 1. the 

ditt.r.noe betweln the 6-ainut. apo.ur •• , and Fl,ure 16 i. the dltt.r.no. ~.twea~ the 3-alnute expo.url.. It i. clear troa the dlttlr.no. ploturl. that at l ... t thl inn.r aaln knot "A" ba. inor •••• d in bri,htn ••• r.l.tiv. 

to tbb ~alo troa 1956 to 1978, .lpeol.11y at polariz.tion P.A. ~350. 

"-1 
Figure 14. M87 mosaic displaying four polarization orientations, each 

in 6- and 3-minute exposures and each at two epochs, 1956 

and 1978 

4- 2 

ORIGINAL 'AM IS 

OF POOR QUALm 
F i UI'C' 1 , Md7 irr ' I',ncc irn :l' " in I h,' S IIl _C' 

in ('OUI' pol. I' j ,ll i 1n lH'i ' nl ;l i l l S , 

::;0 I h,l l I :\!' !\, Lo l1 r Hti In' \ l'Iwd j n 

lin rn in us I '-I , . C,l d) 

Ttl ' ill1 : ';1':, Wt' I',' ~;l' 11 d 

in 1 I'll:, j \ y , Ik r,' I',' Ill',' 
Figure 16. M87 differ ence images in the same format as Fig ure 15 . 

Thesp :Ire 3- mirute exposures . 

4- 4 lIH.GI''tAL PAGE IS 

OF POOR QUALITY 
SECTION V 

PLANETARY NEBULAE - COMPARING EMISSION LINE IMAGES 

In this section. the steps leading toward calculation of the 

volume emission coefficient. temperature. and electron density from 

emission line images of planetary nebulae are described. 

The work in this section was inspired and performed by Peter 

Kupferman of JPL. using the facilities of the Image Processing Laboratory. 

Images were obtained at the Palomar 60-inch telescope with a silicon 

vidicon through interference filters. listed in Table 1. of three 

planetaries NGC7662. NGC6720. and NGC2392. The images comprised 

256-by-256 pixels of 12 bits each at 0.5 seconds of arc per pixel. 

Each image was radiometrically decalibrated by subtracting averaged 

dark current frames and dividing by averaged flat fields obtained during 

the observing run. implying a linear light transfer curve model. All 

of the images for each object were then geometrically registered using 

nearby reference stars unrelated to the nebula. All of the images 

obtained at each wavelength (there were from 2 to 9 redundant pictures) 

were averaged to provide a single picture at each wavelength. A low 

spatial frequency analytical model was generated to match the residual 

background sky level after decalibration. This model was subtracted 

from each image in order to reduce small inhomogeneities in the sky. 

Figure 17 illustrates a mosaic of each of the images for NGC6120 at 

this stage in the processing. Each image is arbitrarily scaled to 

produce a visible pictur. Figure 18 displays the log amplitude of the 

Fourier transform of each of the images in Figure 17. It is evident 

Table 1. Wavelengths of Each Planetary Nebula Image 

0 

Target Line I.D. .\ Bandpass A 

[OIIj 3727 20 

[OIII] 4363 13 

Hell 4686 28 

Hj3 4861 15 

Hel 5876 15 

[OIII] 5007 17 

[Or] 6300 6 

Ha 6563 11 

Ha+[NII] 6563 175 

[SII] 6716 10 

[SIll 6731 11 

5-1 
~ .... .• --- .... - ..... _. - .",,~ •• '"""t ..... ..,. ,-~ ....... -- -.-.~',-. ,T •• + .... '" • , 

from these figures that a periodic pattern due to the deceleration 

grid in tile vidicon (hash lines) and cluster's due to quasi-coherent 

noise are still present to a varying degree in each image. From 

inspection of Figure 18, it was determined that the system MTF went 

to zero at about 0.25 cycles per sample due to atmospheric seeing; 

thus, it was possible to reduce the coherent, periodic, and random noise 

greatly by ccnvolvinG with a band pass filter that suppressed information 

above this frequency. This technique obviated the need for a custom 

modification of each Fourier transform. Figure 19 displays each of 

the rescaled Fourier transforms after convolution, and Figure 20 

illustrates the corresponding smoothed images. 

In order to compute the volume emission coefficient, each image 

was first converted into polar coordinates (Figure 21) in which each 

row represents a radial section outward from the central star, the 

rows extending in azimuth from 00 at the top to 3600 at the bottom. 

If one can assume spherical symmetry, then each row in the polar 

coordinate space would provide a separate model for the nebula, allowing 

different models for different structures at those azimuths. From 

the observed projected radial intensity profiles I(x), one can obtain 

the true radial intensity profile j(r), known as the volume emissivity 

from the Abel transform: 

j ( r) 1 fCO(d I( x) / -2---2-) = - - - _ / x - r dx IT dx V 

r 

from the tr'ue radial emission j(r), one can regenerate the nebula by 

using the inverse polar coordinate transformation. In £"igure 22, the 

positive volume emission coefficient is displayed in red with negative 

regions coded in green. Negative emission indicates where the planetary 

. -,del is not circum ferentially symmetric and that a more sophisticated 

model is desired. 

Absolute calibrations were obtained from spectrophotometry performed 

at specific points in the nebula at the McGraw Hill 52-inch telescope 

at Kitt Peak. The intensities at these points could be used to scale 

trie digital images linearly so that each pixel was known in units of 

ergs/cm2-steradiar-sec, providing units of j(r) in ergs/cm3-steradian-sec. 

rielative photometry is ~ood from 2 to 4 percent, and absolute photometry is 

good from 5 to 8 percent. A map of mean temperCltlire along the line 

of sight can be computed from the ratio of the [DIll) lines 5007 and 

4363 after Usterbrock (Reference 10, p. 100) using the relation: 

T(K) 32900 

= 

(1(5007 ») log (8 ) 

e 1(4363) 

This map is presented in Figure 23. 

5-2 

j 

'j 

, 

·1 

1 

1 

J 

1 

, 

I , 

1 
The electron density could be computed from the (511) lines 6731 

and 6716, using a table caloulated by Osterbrock (Reference 10, p. "2) 

for an assumed temperature of 10~ K. This map is presented in Figure 24. 

The bright r1ngs are artifacts. 

To illustrate the spatial distribution of material in different 

ionization states, the following three figures are presented. Figure 25 

is a mosaio of images in different bands, each oolor coded green, added 

to Ha color coded as red. The relative 1ntensities have been adjusted 

to reveal the most information. In Figures 26 and 27, the ionization 

structure has been enhanced using the HSI transformation (Section VI> 

and assigning three bands to the color primaries blue, green, and red 

according to Table 2. The radial pOSition of each ionization shell 

is apparent. 

Table 2. Color Assignments of Narrow Band Images for 

Figures 26 and 27 

Figure 

26 

27 

Blue 

Hell, 4686 

[OIl] I 3727 

Color Primaries 

Green 

HeI, 5876 

(OIII] , 5007 

Red 

(01], 6300 

[01] I 6300 

These techniques should be applicable to any objects in an optically 

thin, non-LTE environment. 

f " 
r igu r' 17· mos' i c o f nine em ssi on line im;:, s ri c 

an seal i ng for v i · 1 ::1 rpr' a i on . 

i e , n r nd om . ~ is cl t' l Y r obl m ill 

0 im s . 

- 4 II PA E I 

F POOR QUA.LIT\' 
Fig ure 18 . 
Fi ur 1. NGC6720 mos i c o f modi fj d t r ansfonns in h 

as Fi gur 18 . Th coh ren t nois spik s hav 

r due d. each d j splay h s been r no rm al i z d 

no i s r s j d u 1 s . 

5- 6 

ly 
Fig ur O. NGc6720 mosa ic in h s m ur 17 f I' 

h r due i o o f 11 nois OUI'C S 

5- 7 ORIGIN L PA E LS 

Of P R UAW'TY 
Figur 1 • NGCb7 0 

mos 

i e r polar eoordin 

ions 

in the sam 

ord

er as Figure 

20 . 

h \,; n r 1 s r 

ou 

wa rd m p as 

horizon 

fi ur A round n ul 

would r s v i (!. 1 s rue ur 

his o rma 
· . - . 

- ~ - ~ - -T: - - . • - - --= ~~ -- - ~- - - - '" '} 

Figur 

od 

by 

n 

missi o n is r 

symm ry 

v 1 u s 

us 

zimu h. 

"!i 
F1 I.' s 0 11 
. ' 

Fi ur r • '"",' l. 't: .• r" J' 

,"," I. . ' t 1 : I it ' 

7 t\ d f ! 1 f j I ' j 
Figure 25 . NGC6720 mosaic of different images color coded green and 

added to the Hn image coded red. Intensi ties hav e been 

adjusted for viewing. The spatial distribution (in pro- jection) of emitting material is evid ent. 
i"ie;ur" .'b. N i t, ) L')l r'- ,' ,)JL'J r't' IlJd i,m ,1 C i ( tli l\ i ,m :" tr' u,' t ur't' . 

',11 (,r' S ignOlt'n f s .It't bl Ut' = 1Il'11 , IjO: ll; 't't't'tI = tlt'l. 

"t" i t' ; I' ,'d = I Lll 1. t'.'lhl. 1 ,); . h ,IV,' l t't' n t' tlt l ,l lh 't' l1 li S i tI~~ 

t hl' 11 ,' 1 t 1', IIl Sf\l l 'IIl ,lf i " Il. 
I 

J 

, 

Fi g ur e 27 . NG C67 0 color- cod d r nditi on of ionization struc t ure . 

Col or assig nm en s ar e blu = [0 11] , ~7 ; green = [0111 ] , 

5007 ; r ed = LO I ] , 63 00 . Col ors ha ve _een enha nc ed us ing 

t he HSI r ans fo rm at i on. 

5- 14 '-I ~ 
_"""""'!!!'r"'".....,..-,~:l"~-.-:..~~.;: --".. ... ~ .... ~-':..-."'''''"''"'~~ ..... ~'~~''"':~~:- ~~ ........ ~ • ."., .. .,.... ~~ .... ::wtt .... __ .... ,..-". .• -~ -....¥--.-....--~ .... r-... -'--'--~·-:-7 -'." .... --__ --,.-~_.<_.'i' ~-.. " ...... -.~~~~ ""'1-"'"""""f"-=~~ 

.. ";- .. ~,.~ , >.-.~--" ....... , .• ,~.,.>.,'--~~-... -"'"""""'''''~ III! !Il.~' ... _.I%I .. !I ••.••• _ -, ~ 

SECTION VI 

COLOR ENHANCEMENTS 

In Sections IV and V of Reference 1, two powerful tools were 

illustrated for enhancing color differences between multispectral images 

of the same object. In this section, these two techniques (the HSI and 

Principal Component transformation) will be developed further and a third 

technique introduced, called the Log Intensity transformation. All of 

the images in this section were obtained from Dr. Allan Sandage of Hale 

Observatories. The images consisted of four spectral bands, 103aO + WG2, 

103aD + GG14, 103aE + RG1, 103aE + Hu, of M82 obtained at the 200-inch 

telescope. The 103aO image was synthesized from the average of four 

separate exposures, each registered and histogram matched. No correction 

was applied for the HD curve of the emulsion. Each image was linearly 

scaled so that the sky level was equal and the variance of the image 

within the region of the galaxy was also equal (this is equivalent to 

equating the volumes under the polo'cr ~pectra, thus forcing the information 

content of each band to be the same;. The latter constraint is certainly 

not a real one, but it provides a good basis for analysis because each 

image will be represented equally, none being dominated by brighter ones. 

In the remainder of this section, each of the three techniques will 

be applied to the same M82 images so that a comparative evaluation is 

possible. 

A. LOG INTeNSITY STRETCH 

It is possible to vary the dynamic range of a set of multispectral 

images in any fashion whether it be linear or nonlinear and to preserve 

the color information (saturation and hue) by operating upon the intensity 

information only. In this application, it was convenient to reduce the 

dynamic range of the images such that they could be represented in 8 bits 

per pixel, a format compatible with the HSI and Principal Component 

transformations (and within the range of playback devices) to be addressed 

later. Because the majority of the galaxy resided at low intensities, a 

logarithmic compression was selected to reduce the upper dynamic range 

more than the lower dynamic range. Rather than take the logarithm of each 

pixel in turn (with disastrous consequences on the color) the logarithm 

was taken of the sum of each color band at each pixel, providing a scalar 

which could in turn be applied to that pixel location on each picture. 

j=',2, ... ,n (9 ) 

Ij represents the intensity of band j of n bands at one pixel, and C1 

and C2 are constants which control the scaling and linearity respectively. 

'" J£ IS 

,,'';'''~ITY 

6-' 

; 

, 

\ 

~ 
I 

, 

, 

I 

. "t 

FiSure 28 illustrates four oolor oombinations of H82 obtained by seleoting the original four bands, three at a time. The oolor assignments are 

listed in Table 3, and details of the emulsion and filter oombinations 

are shown in Table 4. 

Table 3. Standard Color ASSignments for the H82 Mosaios 

Quadrant 

Upper left 

Upper riSht 

Lower left 

Lower right 

Table 4. 

Emulsion 

103aO 

103aD 

103aE 

103aE 

Blue 

103aO 

103aO 

103aO 

10380 

Color Primaries 

Green 

103aD 

103aD 

103aE 

103aE 

EmulSion/Filter Combinations 

Filter 

WG2 

0014 

RG1 

HQ 

Red 

103aE 

HQ 

HQ 

HQ 

Figure 28 consists of the original intensity images. One can 

distinguish much structure at the center of the galaxy, but not much 

is visible at lower intensities. Figure 29 illustrates the same mosaic 

as Figure 28, but after the Log Intensity transformation. Contrast 

is much lower along the bright bar but lower intensities are more readily 

observed. The color playback device oan be operated under several calibration oonditions. In the case of Figures 28 and 29, the devic~ produced 

a print where equal steps in intensity in each band mapped into equal 

density steps in the photographic negative. This produces a pleasing 

dynamiC range, segregates well between intensity levels in the print, but 

allows some cross talk between the colors so that hue becomes a function 

of intensity. Figure 30 is identical with Figure 29 except that the 

playback device was calibrated to produce a print where the reflectance 

of each step of the gray scale in each band (blue, green, or red) is 

proportional to the intensity of that band. This requirement provides 

an additional logarithmic compression effect, enhancing the lower intensity 

range. Colors should be truer in Figure 30 than in Figure 29. Both 

versions will also be presented later to aid in interpretation. Note 

6-2 

1 

1 
,-

that the Log Intensity stretch has not produced a significant alteration 

of the colors in the scene; it aots as a means of redistributing intensity 

information only. Considerable filamentary detail can be seen in Figure 30, 

detail that remains invisible in Figure 28. 

B. HSI 

The HSI or Hue, Saturation, and Intensity transformation was 

introduced in References 1 and 11 where it was used to enhance color 

differences in NGC1097. Briefly. this transformation attempts to mimic 

the physiological parameterization of the color space from a polar 

coordinate transformation in which intensity is the sum of the three 

spectral bands (blue, green, and red), saturation is the colatitude 

from the gray axis, and hue is the longitude about the gray axis. In 

this section, the HSI transformation will be applied to M82 as a comparison 

with the Principal Component transformation in the next section, but 

also to illustrate some further manipulations of the MSI space. 

The images input to the HSI space are in this case the products of 

the Log Intensity transformation rather than the intensities themselves. 

Figure 31 illustrates a mosaic of the four spectral bands produced by the 

Log Intensity process, in the order upper left = 103aO, upper right = 103aD, 

lower left = 103aE, and lower right = Ha. Subsequent color products will 

be combinations taken three at a time as in Table 3. The HSI processing 

consists of first generating the Hue, Saturation, and Intensity pictures 

from the blue, green, and red inputs. This is followed by performing a 

nonlinear contrast enhancement upon the Saturation picture so that the 

output histogram is equally populated everywhere. An optional step is 

introduoed consisting of performing a low pass filter upon the histogram 

of the Hue picture and then nonlinearly contrast enhancing the Hue 

picture so that the Hue histogram would resemble the low pass filter~d 

version. This last operation, although at first obscure, has a Simple 

function. Concentrations of values in the Hue histogram are caused 

by regions of the pictures which have the same mean wavelength (the 

pattern recognition definition of an object "class"). It would be 

desirable to perform a higher thpn normal contrast enhancement in these 

regions of the Hue histogram in order to improve the disnriminability 

of the eye to color differences within a single "class" of object which, 

because of the clustering of values, probably contains a great deal of 

information. This selective contrast enhancement 1s performea by first 

low pass filtering the Hue histogram, a process which smears or broadens 

the histogram clusters, and then using thts histogram as a model for the 

desired output histogram. The contrast enhancement table generated to 

achieve the desired output histogram is highly nonlinear but is still 

monotonic so that crossovers of color are forbidden. Several advantages 

of this enhancement technique are that the filter preserves the means 

of the clusters; thus. the mean wavelength (mean hue) of the clusters 

is unaltered and the enhancement can be performed automatically. 

Figures 32 through 35 illustrate various stages in the above process 

for each of the four combinations of three colors selected as indicated 

in Table 5. 

6-3 
Table 5. Assignments of Bands to Primaries in Figures 32 through 35 

Color Primaries 

Figure 

Blue Green Red 

32 103aO 103aD 103aE 

33 103aO 103aD Ha 

34 103aO 103aE Ha 

35 103aD 103aE Ha 

In Aach figur", the left column consists of three pictures in 

the following order: top is blue, middle is green, and bottom is red 

after the saturation and hue enhancements. These can be compared with 

the corresponding unenhanoed versions in Figure 31. The right column 

in these same figures oonsists of enhanced HSI images in the following 

order: top is hue, middle is saturation, and bottom is intensity. 

The histograms at the bottom of the left column oorrespond one to one 

with the original unenhanoed versions of the pictures above them. At 

the bottom of the right column of pictures are two oolumns of histograms. 

These are in order from top to bottom: hue, saturation, and intensitYi 

the left column represents the original histograms before enhancement 

and the right column after enhanoement. 

Spikes every 600 in the hue histogram are artifacts due to ooinoidenoes of planes of constant hue with the three-dimensional lattioe 

of 8-bit oolor space. These spikes confuse the operation of the hue 

contrast enhancement and reduoe its effeotiveness. 

Color reconstructions based upon contrast enhanoements of the 

saturation only (no modifioation of the hue) are presented in Figures 

36 and 37 in the order of Table 3. The modified hue images require 

oareful interpretation and thus are not shown as color reconstructions. 

Figure 36 is calibrated with equal intensity steps oorresponding with 

equal density steps and Figure 37 has equal intensity steps as equal 

reflectance steps as previously disoussed. Considerable color structure 

is visible, betraying the spatial distribution of features with similar 

spectral properties. 

For some analyses, the intensity and saturation of a scene proves 

to be a nuisance. In order to see the mean wavelengths residing everywhere 

in the scene, the inverse HSI transformation was performed as usual except 

with both the intensity and saturation images discarded. This produot 

is presented as Figure 38 in the usual Table 3 format. Some regions 

of the image which were too bright or dark to register color before 

are now visible. The sky is Quite complex in hue beoause it has been 

raised above where the true sky level should be in order to observe 

faint struoture, resulting in random noise of all spatial frequencies 

1 

i 

1 

·l 

1 

i 

, 

j 

1 
, t -,*,."...,..."" -'1- JIWf4#11··· e $ 

dominating the 00101'. The hue of a pixel with either an intensity 

or a saturation of zero 1s undefined. 

C. PhlNCIPAL COMPONENT 

The Principal Component transformation was introduced in Reference , as a means of discriminating color structure without neoessarily 

color coding it in a way traceable to the true 00101'. A method has 

been developed (Reference 12) whic:l allows a reconstruotion of the 

approximate colors of a scene after enormous 00101' exaggeration. The 

method does allow some cross talk between 00101' channels and is thus 

dangerous to use if no care is taken in its analysis. but the technique 

provides the most powerful enhanoement available. ihe reasons for 

this can be considered advantageous or disadvantageous depending upon 

onets polnt of view. The reasons are as follows: 

(1) The algorithm performs equally well in discriminating color 

differences even if the images are not properly intensity 

balanced to begin with. 

(2) The technique is not limited to three colors, but can 

operate in a space of dimensionality N where N > 2. 

(3) The process is entirely automated, deriving the optimal 

transformation from diagonalizing the covariance matrix, 

a statistical quantity computed from the images. 

(4) The process formats images in order of desce~~ing information 

content, allowing manipulation of intermediate products. 

briefly, the Principal ~omponent transformation consists of determining that linear transformation (R) between the images which solves 

the set of matrix equations: 

(10 ) 

where K is the covariance matrix of the pictures, t means transpose, 

and K' Is the matrix whose diagonal elements are the eigenvalue solutions 

to the characteristic matrix of K. The enhancement process consists of 

determining the transformation matrix (R) and then of transforming 

the different spectral bands with this matrix into uncorrelated images. 

A mosaic of the uncorrelated images 1s presented as Figure 39. 

The histograms below match one to one with the images above them. 

Considerable detail is evident in these images and it was at this stage 

that the application of this technique stopped in Reference 1. Table 

6 gives the eigenvalues for each of the images of M82 in Figure 39. 

The eigenvalues represent the variance or inforrnat ion content in each image. 

6-5 
Table 6. Information Content in Eaoh Prinoipal Component 

lIIase of M82 for Flaure 39 

Quadrant 

Upper lett 

Upper r1&ht 

Lower lett 

Lower r1cht 

Kiaenvalue 

In order to understand the nature of the imases of Flaure 39 

better, the transformation matrix whioh generated them 1s presented. 

(

Upper left ) Upper right 

Lower left = 

Lower right ( 

0.5118 

-0.4578 

-0.7136 

0.1377 

0.5241 

-0.3456 

0.4792 

-0.6132 

0.5070 

0.0901 

0.4469 

0.7315 

0.4543) 0.8141 

-0.2474 

-0.2639 

(

'03aO) 103aD 

10i~ (11) 

For example, from the matrix, one can see that the upper right imase 

is equivalent to HQ minus the averase of 103aO and 103aD, and that 

the upper left imase 1s essentially the intensity transformation or 

sum of eaoh imase weighted by how well it correlates with the averase. 

The color enhancement oonsists of oontrast enhanoing the prinoipal 

oomponent images using a nonlinear enhancement which fills the output 

histogram so that it has a gaussian distribution, and then performing 

the inverse transformation using (at) back to a recognizable color 

space. In order to understand this process, it 1s important to visualize 

the color space. Because the original input images are highly oorrelated, 

the majority of the color ~pace (N-dimenSional histogram) is populated 

along and around the gra~ .4lCis, leaving empty that portion ot the space 

tar trom the blue = green = ... = red diasonal. Contrast enhancements 

upon the individual color bands assure that the entire diagonal is 

populated but it does little to populate off-axis regions of the color 

space. The Principal COmponent transformation performs a rotation 

of the color space suoh that what was onoe the gray axis (or the major 

information axis) now lies along one of the new axes, eaoh new axis 

in turn being assigned an orthogonal direction through decreasingly 

smaller axes of the color space population until all degrees of freedom 

are exhausted. One oan now see that the first principal oomponent 

image is the intensity (upper left of Figure 39) because it coincides 

with the longest or intensity axis of the oolor spaoe distribution. 

The narrowest axis through this distribution (lower right of Figure 39) 

1s the least ot all correlated directions and contains the least information 

and the most noise. Once the main axis of the oolor distribution has 

been aligned along a new coordinate direction, a oontrast enhanoement 

in the otiler coordinate direotion (other pictures in Figure 39 than 
the upper left) fills the oolor spaoe. The inverse transformation 

using (Rt) re-rotates the oolor spaoe to its oriainal orientation suoh 

that blues return approximately to blues, eto. In the oase of M82, 

all four bands were prooessed simultaneously in this fashion and the 

retransformed Uiases were seleoted in aroups of three for oolor addition 

in a manner similar to Table 3. Filure 40 illustrates the mosaio. 

Considerable oolor struoture oan be seen in the filaments. 

To reduoe the noise level, eaoh of the Prinoipal Component im .. es 

exoept the intensity imase (upper left of Fiaur6 39) was filtered usins 

a tWO-dimensional median filter of a dimension whioh inoreased as the 

information oontent, aiven by the eilenvalue, deoreased. Upon retransformation, 

the oolor-reoombined produots shown in Filure 41 appear softer and 

muoh less noisy. The equivalent operation performed upon the individual 

oolor bands would have soverly dearaded the aalaxy in order to reduoe 

the noise an equivalent amount. 

6-7 
Fi g ur 2 

Mel 

lh 

I ~ , .. ... "'i 

r 
pj 

• 1.'1 , " 

t ; •. 

t i ons . 

m t 

, ,f I 
igur . O. M82 mos i c 

I n 

am n 

s m 

6- 10 
"'t, . , • .. 

3

1 . 

_ 1 
Figur e 32 . M82 mosa i c of hr e spe c ral bands. The left col umn 

r pres n 3 imag s af er color nhancemen from he hue 

sa ura ion and in ensi y ransfo rm ation . The ri ght column 

represen s to = hu. , middle = satura ion , bot om = in ensi y 

afLer con r as nhancemen of t he s urati n and fil 8ring 

of the hue his ogram . His og ram~ benea h he righ column 

of imag es r epr escn hu , sa ura i on , and in ensi y in the 

Ie ft col umn fr uIn op down and h i r enhancemen s in the 

right col umn. fr om op riown , h lef col umn pi c ur s 

a l' e l Oa 0 , 1 0 3a [) , a 1 0 3a E. 

6-1 2 
Figurl' '3 , M ~ mas j 

do wn, th 

in 

1 Ct 

11~ • l f'o l'rn From th or 

1 urnn r j t u r s ::;0 , nd HI , 

b -l 
Fjgur 3 . ,-1 2 Incs.Jic j he. In ~ 

d )wn , tw 1 ~. col umn 

FigUl'C' 

ic ~ 

l't' 1 03aO , 

From h t op 

i 0 : 1:. , a no H l. 
Fi g ') . 

M82 roo 

down , 

fo rm a 

pi c urps CI t' 

Fig t' 10 'aD , 

From 

; 0 '-l E , 

h 0 

nd H I. 
Figur 36, M82 mas ic af er H'I co l or nhancemen wi h hu , sa ura i on , 

ransforma ion and cod d wi h in ensity in equal 

SeT ble 3 fo r col or d sign i ons, The his 0 r ms 

o righ : (op row) hu , sura i on , 

) hu , c n r as - nh nc s ura~i , nd 

con r a int nsi .y ; ( bo am I'O W) blu , r e n , nd r d 

com pon n s of the picture, Comp r his imag wi h Figur 2 ' 

6- 1 
Fi g ur j '( . Md2 mos i c r r WI colo 

xc p with log ill si y 

Th is version rovid · b _ 

color consis nc y ov r h 

for colo r d ions. 

- l'{ 

. J 
r 

I 

E ': _ .. . ~~ . . ... 

.. 

r i g ur e 3 . 

homog n 

o o 

i "A~ .. " . .. ~ ..... . .... 

of pur hu a f r di sc arding h s ur a i on and 

h HS I ransforma i on. The col or o f 

d by r and om fluct ua i ons in h emulsi on 

Ta bl 3 or col or d s i na i ons . 
Figur M82 mos i c 0 

fo ur s ec tr 

in ord I" o f inform ti 011 

t o lowe r ri ht ill r ows s show in 

b c us of colo r diff r nc s n , unliK 

r d . 

- 1 

i 

h or i in 1 b n 
Figure 40 . M82 mosaic of color- nhanced r econstruc i ons fr om the princi pal 

com one n images of Figur 3 See Table 3 for color designanns. Compare wi h Figur s 36 and 37 . 

- ' 0 
... Figure 41. M82 mosa ic of colcr - ennanced imag s prod uced h sam wa y 

as Figure 40 , bu wi th an in t ermedia fil r whi ch smoo h 

in i!1 v ers propo r tion t o h info rma i on co n n o f c h 

pr~!1 ipal componen band . 

ORIG'-'Al PAGE IS 

~ PooR QUALmr 

6- 2 1 
, 

SECTION V11 

DECALIBRATION OF ceD ARRAYS 

An example of the prooedure used to deoalibrate a CCD array is 

inoluded in this seotlon. The array 1n question vas bullt by Texa. 

Instrument. a. part of an lnvestlsation leadins toward the development 

of the apaoe telesoope and Oall1eo senaora (Reterenoe 13). The array 

aufter. trom many deteota whioh w111 not be pre.ent in the tlnal model 

and should not be oonaldered aa a perfeoted devloe. 

Figure 42 illustrates the raw 1mase at a flat fleld produced by 

the CCD. The histograms illustrate the orislnal 1ntensity distribution 

at left and the oontrast-enhanoed di.trlbutlon at r1&ht correapondins 

to the picture above. Several types of artitaot' are present. The 

vertical white linea are due to da.ased pixel a whloh continually senerate 

oharse while the Imas' is being read out vertlcally. The black oolumn 

to the left 1s due to dead pixels whioh oannot transter charse. The 

short vertioal white lines at the top are due to leak .. e of oharse baok 

into the array from the transfer resister at the top. The oorners of 

the frame are saturated and are due to larse blocks of pixels which 

oontinually senerate oharse (even in the dark ourrent). OVerall spatial 

atruoture is due to uneven thlnnlng. The only important con.ideratlon 

i. whether a pixel responds consistently to an exolt1ns atimulua. If It 

does, it can be oalibrated. EVen the linearity of the reaponae is of no 

importance; vid1cons have been routinely calibrated at IPL (Referenoel 

14 and 15) when their response was nonlinear, apatially dependent, a 

function of the spatial struoture of the scene and of prevlous loene •• 

In the case of the CeD, a firat-order correction was applied 

because of the linearity of the devlce. No attempt was made to model 

the leakaae to and trom the transfer register, leavina this atep to 

another alsorithm not addressed here. The calibration oonsista of 

seneratina a large (sreater than 15) number of tlat field frames at 

known exposure values. Dark current trames are subtracted from each 

flat field. For each pixel, a straight 11ne ia tit by leaat squares 

to all of that pixel's values In all of the frames, relatins expoaure 

to response. The coefficienta ot this 11ne are stored in a data.et 

for each pixel. Figures 43 and 44 show pictures of the slope and offaet 

coefficienta of a typical calibratlon tl1e. To decalibrate a frame 

each ~ixel is reverse tranaformed uslna the appropriate coefficients 

and then scaled to the output. 

Fisure 45 contalns the decalibrated version of Flsure ~2. The 

hlstosrams from left to right correspond to the orlslnal scene, the 

decalibrated picture scaled to the same mean value a. the oriSinal frame, 

and the contrast-enhanced frame above. The hi.togram of the decallbrated 

frame i. much narrower, approaohins the Ideal delta function of the true 

input stimulus. Only the random nOise, integer truncation, and blemiah 

structure in the image, which doea not conform to the linear calibration 

model, sive the hiatogram its final ~hape. The RHS error obtained from 

the output hiatosram agrees to within a tew percent of the expeoted 

RHS error from theoretical considerations. The dark corner. of the 

7-1 i 

l --- l~.·"'"'_.~_""'~"""HL""~~~""-"'IIiI'-.:""'IIIX~ .... 1<:...-+ ........ ,..*l1li ..... ·.iiI·.'.. ' .. «.n.5 .. r .... _'m.·' ..... '.. ,;,~· ·•· .. · .. ·6 ..·« .. ·"··.·1 .. " .. '.. '7111· ......... ____ •. _.0 .... 
d.oallbrated tm ... and oalibr.tion til ••• r. due to inad.quate unsaturat.d 

data tor tlttlna :1. lin.ar mod.l. 

A dl.pl.y ot the .tabl1ity ot .aoh pix.l i. pr ... nt.d in Filur. _6. 

Thi. plotur. oont.ln. the v.ri.noe ot •• oh plx.l •• oomputed trom .1x tl.t 

field frame' t.k.n at ld.ntio.l expo.ur. tim... Larl' value. indloat. 

lara. unoertalnty (poor r.p.atability). Notl0' that h1&h variano •• do 

not n.o •••• rl1y oorre.pond wlth bleml.h •• ln Fi,ur. _2. Th. lara' 

ourved oontour. ar. due m.rely to the dynamio rani' .val1abl. to the 

111.... Certaln pix.l. wll1 appear 1 •••• t.bl. lt the fr.otlonal value 

to b. expre •• ed ln lnt ... r form 11 •• 010 .. to the d.oi.lon polnt midway 

b.twe.n two int.,.r •• 

The u.e of l.a.t .quarl. t.ohniq· ... in radlom.trl0 oaUbration 

o.n .11min.t. the nol.e trom o.llbratlon fl1 •• and dark ourrent. allk., 

leavine the nol.e ln the 1 .... a. the only noiae sourc.. Another .dv.ntlle 

ot thl. approach i. that it permits the use of hi,her order funotion. 

than lin.ar to be used to model the 11,ht tran.r.r funotion 1n the 

.v.nt that the dlvioe 1. nonlin.ar. Thla tr ••• one trOll pleo.Wi.e 

oallbration f11e,. 

7-2 

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IPL PIC ID 79/05/24/205919 

'c led d is play o f 

use 0 dec libr a 

h oCfs t t erm o f the calibra io n fi le 

t he CCD image of f i gu r e 42 

7- 5 
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·r - 7 
SECTION VI II 

SUMMARY AND CONCLUSIONS 

From the preoeding sections the following oonolusions have been 

reached. 

(1) The Gull maximum entropy technique of restoring convolved 

imagery is not able to enhanoe resolution more than linear 

techniques. It may, however, prove valuable in analysis 

of objeots whose true nature cannot be predicted because 

it generates images virtually free of artifacts. This is 

not the case for one-dimensional data. 

(2) Maps of the spatial distribution of polarization in galaxies 

can be generated from photographio data if the intensity 

of the images sh~ws differences between intensities or sums 

of intensities that are greater than the RMS noise bars. 

(3) Temporal changes in objects observed over long-time baselines 

can be observed by differencing suitably normalized images. 

(4) Maps of the spatial distribution of ionization, temperature, 

and electron density can be generated for planetary nebulae. 

(5) Investigations of the three-dimensional nature of planetary 

nebulae are possible by observing the value and sign of 

the volume emission coefficient using Abel transformations 

or their equivalent. 

(6) The large dynamic range inherent in galaxies can be reduced 

into the narrower range available for display devices in 

such a way that ~olors in the original scene are not destroyed. 

A logarithmic intensity compression is advantageous for 

galaxies. 

(7) The Hue, Saturation, and Intensity transformation and the 

Prinoipal Component transformation can both be used to 

enhance subtle color differences without scrambling the 

hues in the scene. The latter can optimize the visible 

information content of multispectral images by adjusting 

the transformation to the statistics of the scene. 

(8) ceD arrays can be modeled by least squares generated flat 

field calibration files which offer low noise storage, a 

selection of orders for the function to be used in fitting 

the light transfer curve, and freedom from piecewise-linear 

models. These files decalibrate images to theoretical 

device performance levels. 

8-1 

I 

i 

1 

, 

; 

.; 

I 

1 
REFERENCES 

1. Lorre, J. J., and Lynn, D. J., Application of pigital Image Processing Techniques to Astronomical Imagery 1977, JPL Publication 

78-17, Jet Propulsion Laboratory, Pasadena, Calif., April 15, 1978. 

2. Lorre, J. J., Application of pigital MPage Processing Techniques 

to Astronomical Imagery 1978, JPL Publication 78-91, Jet Propulsion 

Laboratory, Pasadena, Calif., November " 1978. 

3. Gull, S. F., and Daniell, G. J., "Image Reconstruction From Incomplete 

and Noisy Data," Nature, Vol. 272, No. 5655, pp. 686-690, April 20, 1978. 

4. Frieden, B. R., "Restoring With Maximum Likelihood and Maximum Entropy," 

J. Opt. Soc. Amer., Vol. 62, pp. 511-518, 1972. 

5. Frieden, B. R., and Wells, D. C., "Restoring With Maximum Entropy III. 

Poisson Sources and Backgrounds," J. Opt. Soc. Amer., Vol. 68, No.1, 

pp. 93-103, January 1978. 

6. Arp, H., and Lorre, J. J., "Image Processing of Galaxy Photographs," ~, Vol. 210, pp. 58-64, November 15, 1976. 

7. Lorre, J. J., Lynn, D. J., and Benton, W. D., II Recent Developments at 

JPL in the Application of Digital Image Processing Techniques to Astronomical Images," SPIE Conference on Image Processing, Asilomar, California, Vol. 74, pp. 234, February 1976. 

8. Visvanathan, N., and Sandage, A., "Linear Polarization of the Ha 

Emission Line in the Halo of M82 and the Radiation Mechanism of the 

Filaments," ~, Vol. 176, pp. 57-74, August 15, 1972. 

9· Sulentic, J. W., Arp, H., and Lorre, J. J., "Some Properties of the 

Knots in the M87 Jet," AR.!!, in press. 

10. Osterbrock, D. E., Astrophysics of Gaseous Nebulae, W. H. Freeman 

& Co., San FranCiSCO, Calif., 1974. 

11. Lor!"e, J., "Enhancement of the Jets in NGC 1 097 ," .Al2.J., Vol. 222, No.3, 

Part 2, pp. L99-L103, June 15, 1978. 

12. Madura, D. P., Color Enhancement of Landsat Agricultural Imagery, 

JPL Publication 78-102, Jet Propulsion Laboratory, Pasadena, 

Calif., December 15, 1978. 

13. Landauer, F. P., et a1., "An 800-by-800 eeD Imager' for Space-Borne 

Scientific Imaging," GOMAC 1978 Digest of Technical Papers, November 

14-16, 1978. 

14. Soha, J. M., "IPL Processing of the Mariner 1C Images of Mercury," ~, Vol. 80, No.7, pp. 2394-2414, June 10, 1975. 

15. Benesh, M., Voyager Imaging Science Subsystem Calibration Report, 

JPL Publication 618-802, Jet Propulsion Laboratory, Pasadena, Calif., 

July 31, 1978. 

NASA-JPl-Com., l A C.Io' 

",' U S GPO 198G-685-144 

,t ',m-(' 6 

9-1