JOURNAL OF THE OPTICAL SOCIETY OF AMERICA Comparisons of Stellar Scintillation with Image Motion* ROGER HOSFELD Perkins Observatory, Delaware, Ohio (Received August 26, 1953) Stellar scintillation and stellar-image motion are shown by three types of observations to be essentially independent criteria of astronomical "seeing," In particular, it is demonstrated that scintillation is not produced in the immediate neighborhood of the telescope whereas image motion is strongly affected by local air disturbances. It appears therefore that stellar scintillation may be a useful probe for atmospheric studies. INTRODUCTION THE formation of images by astronomical tele- T scopes is impaired by small irregularities in the index of refraction of the earth's atmosphere which cause the images to "dance" about, to become fuzzy and distorted and to undergo rapid fluctuations in brightness. The image motion, or dancing, and the distortions of the image can be studied at the telescope visually and photographically. However, scintillation, specifically defined as the rapid changes in brightness (twinkling to the unaided eye), is visually inconspicuous at the telescope and is most readily observed photoelectrically. All of these variations in the stellar image are loosely described as measures of the quality of the astronomical "seeing." Both image motion and scintillation have been generally regarded as practically equivalent measures of seeing, but several lines of evidence now indicate that these criteria are independent and originate largely in different portions of the light path in the atmosphere. EQUIPMENT AND TECHNIQUE The telescope used in this investigation was the 12.5- inch aperture, 15-foot focal length refractor of the McMillin Observatory. The photoelectric equipment consists of a 1P21 multiplier-type phototube, a cathode- 30 , 030 l PHOTOELECTRIC ARCTURUS 8 SEPT TRACE 235 PM Z=20 z 1. 4 6 8 10 12 14 ANGULAR SEPARATION, SECONDS ARC FIG. 1. Comparison of image motion and scintillation of Arc- turus under widely different conditions. Although the scintillation was much less for the September 8 observations, the motion was greater. * This work was sponsored by the Air Force Cambridge Re- search Center through a contract with the Ohio State University Research Foundation. follower amplifier, and a Brown Electronik Recorder to register the amplified signal from the phototube. Scintillation is revealed by the fluctuations in the recorder trace. The recorder used responds linearly to frequencies from 0 to 10 cps, cutting off sharply at 12 cps. Obviously, only low-frequency scintillation is measured, but it is precisely in the low frequencies that it is at a maximum, is the most easily detected, and causes the most inconvenience in photoelectric ob- servations. Image motion is usually observed with telescopes of small aperture, 3 or 4 inches in diameter, in which stars appear sharply defined, often showing several diffraction rings. Much larger apertures ordinarily give steadier but relatively fuzzier images with diffraction rings seldom visible. The image motion reported here was studied by measuring the changing separations of a pair of extra- focal images of a single bright star, formed by two 3 inch-diameter circular areas on opposite edges of the 12.5-inch telescope lens (Hartmann images). A motion picture camera, with the lens removed, was adapted to the telescope and single frame exposures of 1/25 second duration were taken at 2 second intervals until 100 samples of the spacing of the images were obtained. The spacing varies from instant to instant, and, to the extent that the motions of the star images formed by the two areas are independent, the more unsteady the images the greater is the range of measured separations. The relative independence of the motions can be demonstrated by keeping the telescope stationary while the two extrafocal images drift across a photo- graphic plate. Dependent motion would be indicated by the trails swinging simultaneously from side to side; actually the trails are quite erratic and bear little relationship to each other. The minimum spacing which the images can have occurs when each moves toward the other by its maxi- mum displacement and the greatest spacing results from each having its maximum displacement outward. The difference between the greatest and least spacing is therefore approximately twice the motion of a single image which would be observed in a telescope of 3-inches aperture, or, alternatively, it is twice the diameter of the minimum circle needed to contain all 284 VOLUME 44, NUMBER 4 APRIL, 954
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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
Comparisons of Stellar Scintillation with Image Motion*ROGER HOSFELD
Perkins Observatory, Delaware, Ohio(Received August 26, 1953)
Stellar scintillation and stellar-image motion are shown by three types of observations to be essentiallyindependent criteria of astronomical "seeing," In particular, it is demonstrated that scintillation is notproduced in the immediate neighborhood of the telescope whereas image motion is strongly affected bylocal air disturbances. It appears therefore that stellar scintillation may be a useful probe for atmosphericstudies.
INTRODUCTION
THE formation of images by astronomical tele-T scopes is impaired by small irregularities in theindex of refraction of the earth's atmosphere whichcause the images to "dance" about, to become fuzzyand distorted and to undergo rapid fluctuations inbrightness.
The image motion, or dancing, and the distortions ofthe image can be studied at the telescope visually andphotographically. However, scintillation, specificallydefined as the rapid changes in brightness (twinklingto the unaided eye), is visually inconspicuous at thetelescope and is most readily observed photoelectrically.
All of these variations in the stellar image are looselydescribed as measures of the quality of the astronomical"seeing." Both image motion and scintillation havebeen generally regarded as practically equivalentmeasures of seeing, but several lines of evidence nowindicate that these criteria are independent and originatelargely in different portions of the light path in theatmosphere.
EQUIPMENT AND TECHNIQUE
The telescope used in this investigation was the 12.5-inch aperture, 15-foot focal length refractor of theMcMillin Observatory. The photoelectric equipmentconsists of a 1P21 multiplier-type phototube, a cathode-
30 ,
030
l PHOTOELECTRIC ARCTURUS 8 SEPTTRACE 235 PM Z=20
z 1.4 6 8 10 12 14ANGULAR SEPARATION, SECONDS ARC
FIG. 1. Comparison of image motion and scintillation of Arc-turus under widely different conditions. Although the scintillationwas much less for the September 8 observations, the motion wasgreater.
* This work was sponsored by the Air Force Cambridge Re-search Center through a contract with the Ohio State UniversityResearch Foundation.
follower amplifier, and a Brown Electronik Recorder toregister the amplified signal from the phototube.Scintillation is revealed by the fluctuations in therecorder trace. The recorder used responds linearly tofrequencies from 0 to 10 cps, cutting off sharply at 12cps. Obviously, only low-frequency scintillation ismeasured, but it is precisely in the low frequencies thatit is at a maximum, is the most easily detected, andcauses the most inconvenience in photoelectric ob-servations.
Image motion is usually observed with telescopes ofsmall aperture, 3 or 4 inches in diameter, in which starsappear sharply defined, often showing several diffractionrings. Much larger apertures ordinarily give steadierbut relatively fuzzier images with diffraction ringsseldom visible.
The image motion reported here was studied bymeasuring the changing separations of a pair of extra-focal images of a single bright star, formed by two 3inch-diameter circular areas on opposite edges of the12.5-inch telescope lens (Hartmann images). A motionpicture camera, with the lens removed, was adapted tothe telescope and single frame exposures of 1/25second duration were taken at 2 second intervals until100 samples of the spacing of the images were obtained.The spacing varies from instant to instant, and, to theextent that the motions of the star images formed bythe two areas are independent, the more unsteady theimages the greater is the range of measured separations.The relative independence of the motions can bedemonstrated by keeping the telescope stationarywhile the two extrafocal images drift across a photo-graphic plate. Dependent motion would be indicatedby the trails swinging simultaneously from side toside; actually the trails are quite erratic and bear littlerelationship to each other.
The minimum spacing which the images can haveoccurs when each moves toward the other by its maxi-mum displacement and the greatest spacing resultsfrom each having its maximum displacement outward.The difference between the greatest and least spacingis therefore approximately twice the motion of a singleimage which would be observed in a telescope of3-inches aperture, or, alternatively, it is twice thediameter of the minimum circle needed to contain all
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STELLAR SCINTILLATION AND IMAGE MOTION
the light from a star if the telescope objective has adiameter larger than that covered by the separatedapertures, in this case 12 inches.
OBSERVATIONS
A. Seeing: Scintillation vs Image Motion
Photographically measured image motion and photo-electrically measured scintillation, though often con-cordant, are occasionally in disagreement in theevaluation of astronomical seeing.
An example of discordance is illustrated in Fig. 1.
Arcturus was observed at 8:45 P. M., September 7,1953, 65 degrees from the zenith; then again the nextday at 2:30 P. M. when only 20 degrees from the zenith.If the two photoelectric traces are compared it is seenthat the star was scintillating much less during thedaytime observation, when it was high in the sky. Onthis basis the seeing was best for Arcturus under the
instrument settings10 12 of one component
-2 components
1 component
mey~l *-2 components
FIG. 2. Photoelectric traces of the double star 0 Serpentis(September 16, 1953) showing greater relative scintillation whenone component was observed than when both were observed.The separation of the components is 22 seconds of arc, the magni-tudes 4.5 and 5.4. The phototube gain was adjusted to give com-parable deflections for the two conditions.
X~~~~~~ Castor
- Pollux
FIG. 3. Comparison of the scintillation of the single star Polluxwith the double star Castor at the same distance from the zenith(71 degrees). The components of Castor are separated by 2.6seconds of arc, magnitudes 2.0 and 2.8 (May 29, 1953).
September 8 conditions. If the motion of the images istaken as the criterion, however, quite opposite con-clusions are reached; on September 7 the scintillationwas larger, the image motion less, than on September 8.Clearly some differences must exist in the response ofthese two criteria to the presence of atmospheric in-homogeneities. Additional observations serve to re-solve these differences.
B. Scintillation and Motion of DoubleStar Components
A distinction between the characteristics of imagemotion and scintillation becomes apparent when thebehavior of double stars is examined. If the intensitychanges suffered by the two components are in phase,it follows that the percent scintillation will be the samewhether the components are observed singly or to-gether. If, however, the scintillation is incoherent, somemutual cancellation of intensity changes will occur, re-sulting in reduced percent scintillation for the pair.The double star 0 Serpentis, whose components aresufficiently separated (20 seconds of arc) to be meas-ured individually, gave less percentage variation whenboth components were measured than when only onewas measured. This result is illustrated in Fig. 2. Eventhe much closer double star Castor, 2.6 seconds of arcseparation, showed reduced scintillation when comparedto a single star, Pollux, at the same elevation angle, as
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ROGER HOSFELD
Objective diaphragm
A 1. .A
Extrafocal viewin eyepiece
Fig. 4. Observations of extrafocal images of double stars througha two-aperture objective diaphragm. The distances from A, toA, and from B to B,, are found to vary rapidly, but the distancesfrom A, to B and from A, to B, are unchanging.
shown in Fig. 3. Thus we conclude that the scintillationof double star components of this separation is largelyincoherent.
On the other hand, that the motion of the images ofthe components of these double stars is coherent wasobserved in the following manner: A cardboard dia-phragm with two 3-inch apertures, separated by 9inches, center to center, was placed over the telescopeobjective. When the focal plane of the eyepiece wasdisplaced somewhat from the focal plane of the tele-scope four images were observed, since each apertureformed an image of the double star. Let A and B be thecomponents of the double star, and I and II be theobjective diaphragm apertures. Then, A representsthe image of component A formed by aperture I, B1represents the image of component B formed byaperture I, etc. (see Fig. 4). An examination of thequadrilateral formed by these extrafocal images re-vealed that the sides AA 11 and BBIr are of variable
FIG. 5. Extrafocal images of the double star 0 Serpentis takenwith an aperture of 12.5 inches show identical patterns at anyinstant which are associated with the coherent motions of thein-focus images and are unrelated to the incoherent scintillationof the components. Exposure time one second.
length, while the sides A rBr and A rBII remain un-changed in length and constant in direction.
In short, two closely spaced apertures form images ofa single star which move independently, but a singleaperture forms images of two closely spaced stars whichmove together, or coherently. Such coherent motion ofthe images of the components of double stars is indirect contrast to the incoherent scintillation of thecomponents.
C. Extrafocal Images and IlluminatedObjective Patterns
Since, as we have seen, two small areas of the lensform images of a single star which are subject toindependent motions, it follows that the wave front isnot plane when it arrives at the telescope. Those por-tions of the wave front which are convex will focus ata point beyond the focal plane of the telescope whileconcave portions will come to a focus short of thisplane, leading to an irregular distribution of intensityin extrafocal stellar images. Since this particular non-uniformity is a result of the wavefront deformationassociated with image motion, slightly out-of-focusphotographs of double stars should, in keeping with thecoherence of their motions, at any instant have similardensity irregularities. This expectation is borne out bythe sets of extrafocal images of 0 Serpentis shown inFig. 5. Let us compare these patterns with the in-tensity distributions of starlight at the surface of theobjective itself, sometimes called "illuminated-ob-jective patterns." Such patterns have been wellillustrated by Mikesell, Hoag, and Hall,' Gaviola,2 andothers.
Illuminated-objective photographs are obtained byfocusing a stellar image, formed by the telescope, ontothe lens of a camera which is, in turn, focused on thetelescope objective. The resulting photographs of theobjective show marked irregularities in the distributionof intensity of the starlight, as do extrafocal images,but with an important difference. When the objectiveis examined in the light of a planet (which may beconsidered as an array of starlike points) it is foundthat the patterns are very weak compared to those ofstars (see Mikesell et al.'), from which it can be con-cluded that illuminated objective patterns are notsimilar for adjacent stars, whereas extrafocal imagesare similar.
D. Effects of Local Turbulence on Scintillationand Image Motion
The differences in the observed characteristics of thescintillation of double stars and of the motions ofdouble-star images, as well as the indicated differences
I Mikesell, Hoag, and Hall, J. Opt. Soc. Am. 41, 689 (1951).This very interesting paper on scintillation lists 18 references onthe subject.
2 E. Gaviola, Astron. J. 54, 155 (1949); Popular Astron. 56,353 (1948).
I.
Focal plane -
A,B = double starcomponents
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FIG. 6. Three star trails, from exposure on the Pleiades, adjusted to coincide in position. The top and bottom trailsare more than 0.5 degrees apart in angular distance. The circular images were impressed on the plate to mark the in-
troduction of warm air into the dome to initiate local turbulence. All trails are identically affected.
between the patterns of the illuminated-objective andthose of the extrafocal images, can be explained byconsidering scintillation to be caused by atmosphericturbulence at a greater distance from the telescopethan that responsible for image motion. This suggests asimple experiment to determine the relative influence ofsurface turbulence on scintillation and image motion.The results provide conclusive evidence of the inde-pendence of these two criteria of seeing.
The experiment consisted of suddenly introducingwarm air from the interior of the observatory (30degrees F higher than that in the dome and outside)into the telescope room and recording its effects onimage motion and scintillation.
The effect upon image motion is shown in Fig. 6.The three star trails were taken from an exposure ofthe Pleiades cluster for which the full aperture of thetelescope was used. The trails were produced by thediurnal motion of the stars, the telescope remainingstationary. The circular images mark the instant atwhich warm air was allowed to enter the dome. Atthat time the images were unquestionably set intoviolent agitation, and further, these motions were iden-tical over the entire field of one degree. The appearanceof the trails also seems to indicate greatly increasedscintillation but this, too, is the result of the erraticmotions of the images, as the following figures prove.
The recorded photoelectric signal from Capella isshown in Fig. 7 as the experiment is repeated to deter-mine whether scintillation is affected. Certainly no largechange in scintillation, comparable to the change inimage motion, is evident.
To discover next whether small changes in scintilla-tion may have occured, the following was done. A well-known characteristic of scintillation is that associatedwith source area, namely, the larger the angulardiameter of the source, the smaller the scintillation.3' 4
Jupiter, for example, which has a diameter of about40 seconds of arc, scintillates much less than a star.But, it will be recalled that the large apparent intensitychanges in the star trails in disturbed air (Fig. 6)occurred simultaneously over a field of one degree, and
I M. A. Ellison and H. Seddon, Monthly Notices Roy. Astron.Soc. 112, 73 (1952).
4 E. Goldstein, NRL Report N-3710 (1 July, 1950).
persisted for a few tenths of a second. Therefore, anylocally produced changes of intensity should be asgreat in absolute value for Jupiter as for a star andmore easily discovered because of the small initialscintillation of Jupiter. Variations in brightness assmall as 1 percent, persisting for only 0.1 second,should be detectable. Figure 8 shows the photoelectrictrace of Jupiter before and after introducing warm air;but no difference in scintillation is observed. Thesignal from a dc lamp shows that instrumental noisewas not masking any changes which might haveoccurred.
Finally, it is conceivable that small areas of thetelescope lens may have experienced increases inscintillation which were averaged out over the fullaperture. Figure 9 shows the result of observingSirius through a one inch objective diaphragm. The
FIG. 7. Photoelectric signal of Capella (February 9, 1953)showing no effect of local temperature gradients on stellar scin-tillation. The interruptions of the trace were caused by insertinga mirror which permits visual inspection of the image. Aperture= 12.5 in.
FIG. 8. Photoelectric trace of Jupiter showing no effect of localturbulence on the signal from an extended source.
signal once again was unaffected by the local turbu-lence.
CONCLUSIONS
The observations described lead to the conclusionthat temperature discontinuities in the air near thetelescope do not affect the total brightness of the imageas recorded photoelectrically, even when the tempera-ture differences are severe enough to accentuategreatly the image motion and to destroy telescopicdefinition. Consequently, it is clear why motion andscintillation do not necessarily give compatible resultsin evaluating seeing.
The observations of double-star components, de-
-dc. lamp atSirius settings
7:0 PM
10 2
7:45 PM
11-4 6PM~f;F0f0:
- Warm air admittedto dome
TONf '.A00t
FIG. 9. Photoelectric signal of Sirius (February 22, 1953)showing no locally produced changes in scintillation over anobjective area one inch in diameter.
scribed earlier, are also consistent with the view thatscintillation is the result of turbulence at a greaterdistance from the telescope than that causing imagemotion. Since scintillation appears to be unaffectedby surface conditions it should be a useful atmos-pheric probe.
ACKNOWLEDGMENTS -
The author is grateful to Dr. J. Allen Hynek whocontributed much to the preparation of this paper,and to Mr. William M. Protheroe who constructedand modified the electronic circuitry.
