Extending the Stellar Field of View of Ritchey-Chretien Telescopes Seymour Rosin and Max Amon The preferred modern type of large telescope today is the Ritchey-Chretien form. The field size is aberrationally limited by undercorrected astigmatism and field curvature. A pair of equally and op- positely oriented flat transmittng plates can neutralize either or both of these aberrations locally in the field to restore the image. These plates, relatively inexpensive and positionally noncritical, may be used to extend the available image area by an order of magnitude. 1. Introduction and Purpose During the first half of the twentieth century, the favored form of large telescope employed the parab- oloid as the primary mirror. A hyperbolic secondary mirror was used to redirect the light back through a hole in the primary to form the Cassegrain focus. For both the prime focus and the Cassegrain focus, the extent of the field of view is limited by coma. The heavy coma of a paraboloidal mirror used at prime focus is well known, and that of the Cassegrain focus is equal to that of a simple paraboloid of equivalent aperture and focal length. For a variety of reasons, the most useful focus of a large telescope is the Cassegrain focus. The coma of the classical Cassegrain telescope may be eliminated by changing the telescope form from the paraboloid- hyperboloid combination to the Ritchey-Chretien form. Here the paraboloid becomes a weak (low eccentricity) hyperboloid, and the secondary alters its hyperbolic form to restore freedom from spherical aberration. The-field of view of the Ritchey-Chretien telescope is thus substantially better than that of the classical Cassegrain, so much so that practically all modern telescopes are of this type. The improvement is shown dramatically in an article by Schulte,' where Fig. 1 of his article compares the blur circles of a classical Cassegrain and of a Ritchey-Chretien telescope using, for purposes of this comparison, the constructional data of the 84-in. (213-cm) Kitt Peak telescope. The blur circles were evaluated at 10 min and 15 min off axis. The preference for the Ritchey-Chretien form of telescope by the scientific investigators conducting astronomical experiments is well established. It is natural, therefore, to consider means by which the The authors are with Kollsman Instrument Corporation, Syos- set, New York 11791. Received 23 July 1971. useful field of the Ritchey-Chretien may be extended still further. The most obvious method is to design a so-called field corrector, which takes the form of a group of refracting elements located in the region just forward of the focal plane. Another paper by Schulte 2 is an excellent summary of such corrector systems proposed for this purpose. Further references 3 - 8 are also listed at the end of this article. This paper describes a method entirely different in concept from the field correctors mentioned in the pre- vious paragraph. Instead of using large refracting elements to correct the entire field of view all at once, it employs a reasonably simple optical device to correct the system locally over a limited but not negligible region. This device is small, relatively inexpensive, and noncritical positionally in all three dimensions. II Discussion While the device to be described may be used with any Ritchey-Chretien system, we will, for purposes of illustration, apply it to correct the field of the 84-in. (213-cm) Kitt Peak telescope discussed by Schulte in Ref 1. For purposes of ready reference, the system data will be given again. Figure 1 shows this schematic- ally, with the data given in Table I. It will be recalled that Schulte gave data for the blur diameter at 10 min and 15 min off axis for the uncorrected system. We will arbitrarily extend our interest to 45 min off axis. A Coddington calculation for the tangential and sag- ittal foci of the system of Table I yields the values in centimeters as shown in Table II. In Table II, the first column gives the field points as a fraction of 45 min; the second and third columns, the positions of the tangential and sagittal foci as referred to the paraxial focal plane; and the fourth column, their difference. The negative values associated with the (T - S) values indicate the presence of so-called undercorrected astigmatism. Any device we may propose must serve to neutralize this aberration. Consequently, we may ask ourselves July 1972 / Vol. 11, No. 7 / APPLIED OPTICS 1623
Transcript
Extending the Stellar Field of View of Ritchey-Chretien Telescopes
Seymour Rosin and Max Amon
The preferred modern type of large telescope today is the Ritchey-Chretien form. The field size isaberrationally limited by undercorrected astigmatism and field curvature. A pair of equally and op-positely oriented flat transmittng plates can neutralize either or both of these aberrations locally in thefield to restore the image. These plates, relatively inexpensive and positionally noncritical, may beused to extend the available image area by an order of magnitude.
1. Introduction and PurposeDuring the first half of the twentieth century, the
favored form of large telescope employed the parab-oloid as the primary mirror. A hyperbolic secondarymirror was used to redirect the light back through ahole in the primary to form the Cassegrain focus.
For both the prime focus and the Cassegrain focus,the extent of the field of view is limited by coma. Theheavy coma of a paraboloidal mirror used at primefocus is well known, and that of the Cassegrain focus isequal to that of a simple paraboloid of equivalentaperture and focal length.
For a variety of reasons, the most useful focus of alarge telescope is the Cassegrain focus. The coma ofthe classical Cassegrain telescope may be eliminated bychanging the telescope form from the paraboloid-hyperboloid combination to the Ritchey-Chretienform. Here the paraboloid becomes a weak (loweccentricity) hyperboloid, and the secondary alters itshyperbolic form to restore freedom from sphericalaberration. The-field of view of the Ritchey-Chretientelescope is thus substantially better than that of theclassical Cassegrain, so much so that practically allmodern telescopes are of this type. The improvementis shown dramatically in an article by Schulte,' whereFig. 1 of his article compares the blur circles of a classicalCassegrain and of a Ritchey-Chretien telescope using,for purposes of this comparison, the constructionaldata of the 84-in. (213-cm) Kitt Peak telescope. Theblur circles were evaluated at 10 min and 15 min offaxis.
The preference for the Ritchey-Chretien form oftelescope by the scientific investigators conductingastronomical experiments is well established. It isnatural, therefore, to consider means by which the
The authors are with Kollsman Instrument Corporation, Syos-set, New York 11791.
Received 23 July 1971.
useful field of the Ritchey-Chretien may be extendedstill further. The most obvious method is to design aso-called field corrector, which takes the form of a groupof refracting elements located in the region just forwardof the focal plane. Another paper by Schulte2 is anexcellent summary of such corrector systems proposedfor this purpose. Further references 3-8 are alsolisted at the end of this article.
This paper describes a method entirely different inconcept from the field correctors mentioned in the pre-vious paragraph. Instead of using large refractingelements to correct the entire field of view all at once,it employs a reasonably simple optical device to correctthe system locally over a limited but not negligibleregion. This device is small, relatively inexpensive,and noncritical positionally in all three dimensions.
II DiscussionWhile the device to be described may be used with
any Ritchey-Chretien system, we will, for purposes ofillustration, apply it to correct the field of the 84-in.(213-cm) Kitt Peak telescope discussed by Schulte inRef 1. For purposes of ready reference, the systemdata will be given again. Figure 1 shows this schematic-ally, with the data given in Table I. It will be recalledthat Schulte gave data for the blur diameter at 10 minand 15 min off axis for the uncorrected system. Wewill arbitrarily extend our interest to 45 min off axis.A Coddington calculation for the tangential and sag-ittal foci of the system of Table I yields the valuesin centimeters as shown in Table II.
In Table II, the first column gives the field points asa fraction of 45 min; the second and third columns, thepositions of the tangential and sagittal foci as referredto the paraxial focal plane; and the fourth column,their difference. The negative values associated withthe (T - S) values indicate the presence of so-calledundercorrected astigmatism.
Any device we may propose must serve to neutralizethis aberration. Consequently, we may ask ourselves
if there exists an optical device which inherently im-parts overcorrected astigmatism into ray bundles.One such is an inclined glass plate.
For many years, we, in common with most opticaldesigners, have wished to use inclined glass plates inconvergent space, particularly for use as beam splitters,but have been frustrated by the substantial centralastigmatism produced by them. Here we wish to seeif we can use this astigmatism in a positive sense tocancel that of the Ritchey-Chretien telescope.
We turn now to a qualitative discussion of theproperties of an inclined flat plate, particularly itsaberrations. We list these as follows, dividing theminto axial and transverse aberrations. Axial aber-rations: (1) spherical aberration, (2) axial color, (3)astigmatism. Lateral aberrations: (1) displacementof line of sight, (2) coma, (3) lateral color, (4) dis-tortion.
Among the axial aberrations, spherical aberrationand axial color will be minor at the moderate platethicknesses with which we will be concerned, andonly astigmatism is substantial in amount. All thelateral aberrations are large and harmful to our pur-pose. It is to be noted that Fig. 2 shows the platerotated an angle a clockwise from the zero positionnormal to the indicated ray. If the plate had been
rotated an equal angle counterclockwise instead, theaxial aberrations would be unchanged, while the lateralaberrations would be reversed in direction.
These considerations provide us with the clue for theelimination of the lateral aberrations. If we dividethe plate into two equal parts and rotate them equallyin opposite directions, the lateral aberrations willcancel, while the axial aberrations, particularly theastigmatism, remain unchanged. The arrangement isshown in Fig. 3.
Using the well-known Coddington equations, wemay derive expressions for the astigmatism (T - S) pro-duced by the plates, and for the shift As of the sagittalfocus as a function of tilt angle. These expressions are
T -S = [(n' - 1) sin2Ca/(n' - sin2e) f]2d. (1)
Here n is the index of the plate, a the angle of the tilt,and d the thickness of each plate. Also
where As is the shift in sagittal focus.Both of these expressions are independent of the
position of the focus so that the plates may be placedanywhere in the convergent beam. Of course, themost convenient position for our application is just infront of the focal plane, where the required aperture issmall. The location is noncritical in the z direction(along the ray) and obviously also in the x and y direc-tions. As one consequence, the point of rotation ofeach plate may be at any desired location relative tothe plate.
/72d
Fig. 2. Ray traversing inclined plate.
d a
Fig. 3. Ray traversing plate pair.
1624 APPLIED OPTICS / Vol. 11, No. 7 / July 1972
Table Ill. Astigmatism Expressed as Coefficient of 2d
ag n = 1.4 n = 1.5 n = 1.6 n = 1.7 n = 1.8 n = 1.9
In order to see the nature of the functions repre-sented by Eqs. (1) and (2), we form Tables III and IV,which are the calculations of the bracketed coefficientof the total glass thickness 2d.
One may be tempted to think that the astigmatismwould vary decidedly with color (index), but Table IIIshows that this is far from the case. The amount ofastigmatism is a slowly varying function of n, with abroad maximum for any given tilt value of the plates.The change for any given material over its range oftransmittance is so small as to be quite negligible.
The maximum may be found by differentiating Eq.(1). The equation giving this maximum is, then,
n' = 3 - 2 sin'a. (3)
Listing values obtained from Eq. (3), we have thefollowing:
a (degrees)15304560
n
1.6931.5811.4141.225
Thus, at high tilt angles, the maximum value of astig-matism occurs at low values of index, a somewhat un-expected result.
Turning to a consideration of Table IV, we note thatthe shift in sagittal focus is relatively small, particularlyat low index values.
As a result of these considerations, we have chosenfused quartz, a low index material, as the exampleillustrating the device, and we have decided tem-porarily to restrict the maximum tilt to 450. Ofcourse, the choice of material would be governed by theneeds of the observer and the transmission range ofinterest.
Setting n = 1.45845 (the index of quartz at X =5876 A) and a = 450, we obtain from Eq. (1) T - S =0.27153 (2d).
Equating this to the undercorrected astigmatism ofthe telescope at 45 min as listed in Table II, we obtain2d = 0.79860/0.27153, or d = 1.47 cm.
111. Results
At the end of the last section, we calculated the platethickness required to correct the astigmatism of theRitchey-Chretien 45 min from the axis. By moving theplates in a scissorlike fashion, we may vary the angleformed by the plates. The angle may be set as a func-tion of the radial position of the plates from the opticalaxis. It should be noted from Table III that theamount of astigmatism introduced by the plates isapproximately proportional to the square of the tiltangle. The astigmatism of the Ritchey-Chretien isproportional to the square of the field. Therefore, adirect proportionality exists between the tilt requiredfor the plates and its position in the field. Figures 4(a)and (b) show this proportionality clearly. The astig-matism introduced by the plates is approximately equaland opposite in sign to that of the Ritchey-Chretien.
Figure 5 shows the plates in the path of an off-axisbundle. Strictly speaking, the plates should be ori-ented symmetrically with the chief ray, but this isnot necessary and the 450 equal and opposite tilts arewith respect to the optical axis. For the 213-cm tele-scope, the 45-min image point is approximately 21.2cm from the axis.
The effectiveness of the plates is clearly demon-strated by means of spot diagrams. The latter arecomputer-drawn with the aid of Gordon Spencer's raytrace program GOALS (Geometrical Optical Analysisof Lens Systems).
Figure 6(a) gives the spot diagrams on a flat focal plane,coincident with the paraxial focus of the telescope aloneat 15 min, 30 min, and 45 min. Figure 6(b) representsthe same taken on the surface of best focus, halfwaybetween the sagittal and tangential surfaces. It is tobe noted that they are smaller than those of Fig 6(a)and are symmetrical.
When we add the plates to the system, we obtainFigs. 7(a) and (b). Figure 7(a) gives the spot diagramson the flat paraxial focal plane. It is to be noted, incontrast to those of Fig. 6(a) that they have becomecircular. Figure 7(b), taken along the curve of best
July 1972 / Vol. 11, No. 7 / APPLIED OPTICS 1625
TILTED PLATES
lii- FOCAL SURFACE
1\STIGMATISM T-S) IS CIIIIEMl
Fig. 4. (a) Field angle of the Ritchey-Chretien vs astigmatism.(b) Tilt angle of the inclined plates vs astigmatism.
FIELD AiGLE 15 MIN 30 MIN
Fig. 5. Schematic representation of plate position.
This surface of best focus is coincident with a spher-ical surface whose curvature is identical with thesagittal curvature of the Ritchey-Chretien telescope.This is, of course, to be expected, since the plates have,as has been noted, only a small effect o the sagittal
field. It is also important to note that all three spotdiagrams were taken with the same 1.47-cm plates.The latter were oriented at 450 for the 45-min position,at 300 for the 30-min position, and at 150 for the 15-min position. Hence, we conclude that the propor-tionality of plate tilt with angular field is fulfilled quitewell.
It is to be noted that all the spot diagrams were
1626 APPLIED OPTICS / Vol. 11, No. 7 / July 1972
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(b)made using one hundred rays in each of the wave-lengths corresponding to C, d, and F light. Theeffects would not have been appreciably different hadthe wavelengths been chosen anywhere within thetransmission range of fused silica.
One can conceive, then, of a pair of plates of thisgiven thickness in a mechanical arrangement wherebythe tilt angle may be varied, and of adjusting the tilt inaccordance with the field angle, the local image planeto be located along the over-all sagittal curve.
This need not be the only way in which to designand use the plates, however. It may, for example, befound desirable to flatten the image surface by meansof a negative field lens. Here the power of the fieldlens will be that required to flatten the sagittal field.The design of the plates will be affected by the powerand location of the field lens. However, we havetested the system for particular values, and there is nodifficulty in obtaining point images along a flat planeout to 45 min.
Another possible arrangement is to provide a fieldlens to turn the chief rays parallel to the axis (a so-called telecentric system). This will, in general, re-quire a positive field lens, adding to the sagittal cur-vature. This arrangement is desirable if a relaysystem is needed to change the magnification. Here,again, point images will be obtained.
A most interesting arrangement occurs if one chooses
to compensate the astigmatism by plates of differentthickness locally over the field. One is at liberty tochoose this thickness to compensate for the sagittalcurvature at any desired field angle, and thus to makethe focal plane flat in space. How this is done may beillustrated in Fig. 8, where we show the flat plane coin-cident with the uncorrected paraxial focal plane.
In Fig. 8(a), we show the sagittal focus S in advance ofthe paraxial focal plane. Inserting the plates at zerotilt has the effect of displacing S back toward P, andthis displacement x will be given by
x = 2[(n - 1)/n]d, (3)
where d is the thickness of each plate. For fusedquartz, x = 0.62868d.
Suppose now that we wish this displacement toequal the sag of the sagittal focus at 45 min. FromTable I, this value is 0.86441, whence we calculate the
(a) (b)
Fig. 8. Correction of field curvature by plates.
July 1972 / Vol. 11, No. 7 / APPLIED OPTICS 1627
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value of d to be 1.375 cm, somewhat thinner than the1.47 cm used earlier. We also note that the astig-matism from Table I, at 45 min, is -0.79860. Sub-stituting these values in Eq. (1), we obtain
0.79860 = [(n2- 1) sin2a/(n 2 - sinac)§] 2.75.
Solving for a, we get a = 46.340.In order now to test our theory, we traced a bundle of
rays through the system including a pair of plates eachtilted 46.34° and each 1.375 cm thick. The spotdiagram is evaluated at the original Ritchey-Chretienparaxial focus. The result of this trace is shown inFig. 9(a). Figure 9(b) shows the spot diagram at 44min off axis traced through the same plates, and Fig.9(c) shows the results of a bundle traced at 45 min witha 1-min displacement in the sagittal direction. Wetherefore conclude that the local field has a radius ofapproximately 1 min within which the resolution willstill be of the order of 1 sec.
We have repeated this procedure for a 30-min field.The sag of the sagittal field is proportional to thesquare of the field angle, so that at 30° we would re-quire plates (2/3)2 = 4/9 as thick to set the focus atthe paraxial focal plane. This thickness is, then,0.6111 cm. Since the astigmatism is proportional tothe square of the field [see Eq. (1)] and proportional
,,,--- 1 .,. 1, .....(f)
4 MIN OFFCENTER
SAGITTAL
I Iil I)I 0Rafe
I ii';T+Fl
I04i)
Fig. 9. Ritchey-Chretien plusplates evaluated on a flat focalplane located at the paraxialfocus: (a) center, (b) 1 min offcenter tangential, (c) 1 min offcenter sagittal, (d) center, (e)2 min off center tangential, (f)2 min off center sagittal, (g)center, (h) 4 min off center tan-gential, (i) 4 min off center sagit-
tal.
to the plate thickness, it follows that the requiredplate tilt at 30 min is unchanged from that at 45 min.Spot diagrams are shown at 30 min [Fig. 9(d) 1, at 28 min[Fig. 9(e) , and at 30 min with a 2-min sagittal displace-ment [Fig. 9(f) ], where by we estimate the focal fieldextent to be 2 min in radius.
Finally, similar data are given for 15 min from the axis[Figs. 9(g), (h), (i)]. The plates are still oriented at thesame angle, but are only 0.153 cm thick. The localfield of view is estimated in excess of 4 min in radius.
IV. Conclusions and SummaryThere is no doubt that the simple and noncritical
plate assembly described in this paper is effective inneutralizing the local field astigmatism of Ritchey-Chretien telescopes so as to make available a usefulimage area increased by approximately one order ofmagnitude over that available with an uncorrectedtelescope. While the calculations have been madewith regard to the Kitt Peak, 84-in. (213-cm) instru-ment, there is no loss of generality, since the astigmaticerror of other Ritchey-Chretien telescopes limitinguseful field will all be similar in amount.
The concept of this device was initiated during astudy program carried out at Kollman InstrumentCorporation for the requirements of an unmanned
1628 APPLIED OPTICS / Vol. 11, No. 7 / July 1972
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space telescope, and the specific application was to in-crease the available field for offset fine guidance,whereby the likelihood of finding suitable guidingstars is enhanced by this increase in available field.For this application, it is conceivable that a single pairof plates, with inclined angles proportional to the field,may be properly positioned by a suitable designed mech-anism, together with a suitably positioned detector.
For manned vehicles and for ground-based tele-scopes, the device probably could have the alternateform; that is, to tailor the thickness of the plates toshift the focus to a single over-all flat plane, which mayor may not coincide with the uncorrected paraxialfocal plane. It is certainly no great task to plan theexperiment in advance, construct a pair of plates to
suit, and suitably position them in the instrument byrelatively crude means. Here we find not only a solu-tion for fine guidance, but also a method of performingseveral investigations simultaneously.
References1. D. H. Schulte, Appl. Opt. 2, 141 (1963).2. D. H. Schulte, Optical Telescope Technology, NASA SP-233
(GPO, Washington, D.C.), pp. 327-334.3. J. Landi-Dessy, A. Puck, and J. M. Simon, Mem. Soc. Auto.
Ital. 38, 1 (1967).4. H. Kohler, Appl. Opt. 7, 241 (1968).5. S. Rosin, Appl. Opt. 5, 675 (1966).6. R. N. Wilson, Appl. Opt. 7, 253 (1968).7. C. G. Wynne, Appl. Opt. 4, 1185 (1965).8. B. J. Howell, Appl. Opt. 8, 686 (1969).
OBJECTIVE
This is the third international conference devoted tobeam-foil spectroscopy. The first was held in Novem-.ber 1967 in Tucson, Arizona; the second in June1970 in Lysekil, Sweden. The forthcoming meetingwill be of interest to scientists whose research effortsare in the field of beam-foil spectroscopy and tothose who contemplate establishment of researchprograms in this field. The Proceedings will bepublished by Nuclear Instrunents and Method&
SCIENTIFIC AND TECHNICAL SESSIONS
Invited and contributed papers will be presented insuch areas as: lifetime measurements, spectra,g-values, quantum beats, Hanle effect, magnetic reso-nances, eeman effect, beam-foil X rays and elec-trons, element abundances, and problems of the solarsystem, as well as the list of subjects on which theinvited speakers have agreed to speak.
INVITED PAPERS
Thirty minutes' presentation time will be allotted toeach invited paper, with an additional ten minutes fordiscussion. A partial list of the invited speakers andtheir subjects is given below. The complete list ofinvited speakers will be mailed to each pre-registrant.
Beam-Foil Spectroscopy with Low-Energy Accelera-tors
T. AndersenUniversity of Aarhus
Quasars and NeutrinosJ. N. BahcallCalifornia Institute of Technology
Survey of Beam-Foil SpectroscopyS. BashkinUniversity of Arizona
Optical Spectra from Highly Ionized AtomsJ. BromanderUniversity of Uppsala
g-ValuesD. Church and C. H. LiuUniversity of Arizona
Lifetimes of Metastable Levels in Atoms and Mole-cules
A. CorneyOxford University
Theory of Rare-Earth Level StructuresR. D. CowanLos Alamos Scientific Laboratory
Oscillator Strengths and AstrophysicsA. DalgarnoHarvard University
Lifetime DataM. J. DufayUniversity Claude Bernard
Particle Interaction TheoryJ. D. GarciaUniversity of Arizona
Fine StructureT. HadeishiUniversity of California, Berkeley
Lineshapes and Charge IdentificationJ. A. LeavittUniversity of Arizona
one- and Two-Electron Beam-Foil SpectraR. MarrusUniversity of California, Berkeley
New Term Schemes1. MartinsonResearch Institute for Physics
Oscillator Strengths0. SinanogluYale University
Spectrum of the Solar CoronaK. WidingNaval Research Laboratory
CALL FOR CONTRIBUTED PAPERS
A limited number of contributed papers coveringoriginal work on the conference subjects will beaccepted for presentation. Presentation time forcontributed papers will be twenty minutes, with tenadditional minutes for discussion. Authors shouldsubmit a 200-word abstract, which should be typeddouble spaced on one side of a single B%/ by 11-inchsheet of white bond paper with one-inch margins allaround. The abstracts of accepted papers will bereproduced directly by photo offset, so all equations,references, etc. must appear on the page exactly asthey are to be reproduced. Begin the page with thetitle of the paper, follow ihe title with your name andaddress, then the body of the abstract.
All abstracts must reach us before August 1, 1972.Mail them to:
Professor S. BashkinDepartment of PhysicsUniversity of ArizonaTucson, Arizona 85721,
Authors will be notified whether their papers hvebeen accepted within two weeks of receipt of theirabstracts. The abstracts of accepted papers will bereproduced and distributed at the meeting.
PROCEEDINGS
All accepted papers and the accompanying discus-sions will be published in the Proceedings of theConference, which will appear in Nuclear Instrumentsand Method The complete manuscript of each papershould be given to Professor Bshkin before theconference closing date, October 6, 1972. Authorswill have the opportunity to correct proofs of theirpepers. Papers submitted for the Proceedings shouldbe in English.
REGISTRATION FEE
There will be a registration fee of $45, of which $12will be used to provide each registrant with a copy ofthe Proceedings.
