Orthogonal Mirror Telescopes for X-ray Astronomy L. P. VanSpeybroeck, R. C. Chase, and T. F. Zehnpfennig Crossed mirror telescopes are presented as an alternative to the present telescope systems used in x-ray astronomy. These instruments generally have a higher x-ray collecting efficiency but a poorer angular resolution than the more conventional paraboloid-hyperboloid telescopes. They also can be made more easily and quickly as was demonstrated by a recent rocket flight that used a simplified mirror design with only one-dimensional focusing. The application of focusing x-ray optics to x-ray astronomy was first discussed by Giacconi and Rossi.' Since that time much work has been done on grazing incidence imaging systems. The most commonly used system consists of two successive conic sections of revolution.', 3 Telescopes of this geometry have been used with great success for obtaining high resolu- tion photographs of the sun in x-rays. 4 ' Fisher and Meyerott 6 have built another type of system with one- dimensional focusing which is composed of reflecting parabolas of translation. A system of one-dimensional focusing has recently been flown successfully in a sounding rocket by Gorenstein et al. 7 ; during this flight x-ray images of the Cygnus Loop were obtained. As an alternative to the present instruments, we have designed several telescope configurations that focus the x rays with sets of two orthogonal parabolas of translation. The use of crossed mirrors for x-ray focusing was first proposed by Kirkpatrick and Baez." McGee successfully demonstrated the use of crossed- spherical reflectors in an x-ray microscope. 9 A simplified Kirkpatrick-Baez device is shown in Fig. 1(A). The incident ray successively strikes two parabolas at approximately right angles to each other. In practical designs, the surface area is increased by using many approximately parallel parabolas as in Fig. 1(B). All authors were with American Science and Engineering, Cambridge, Massachusetts 02142, when this work was done; T. F. Zehnpfennig is now with Visidyne, Inc., Woburn, Mas- sachusetts 01801. Received 18 September 1970. The equations for the individual surfaces can be written: = pi' + 2Pl(Zl + a), Y2 = P,' + 2P2Z2, Y, arbitrary, (1) X2 arbitrary, (2) where Z is the symmetry axis, the focal plane is at Z = 0, and the x rays first strike the surface described by Eq. (1). P 1 , P 2 , and a are constant parameters. The displacement of the focus of the first parabola is neces- sary because of the second reflection, and optimum focus is achieved when a = P 2 . This condition cannot be exactly achieved if many approximately parallel surfaces are used to reflect in the Y-Z plane since such surfaces necessarily have different values of P 2 . In this case we set a equal to the average value of P2. If a P, the resolution is primarily determined by the length of the mirror segments; neglecting all correction small compared to the effects determined by the length of the mirror section, we obtained the following approximate (see next paragraph) intersection of a ray in the focal plane: yF = f(l - A) tanG sin+, YF = f(l + Al) tanG sinj ± f (X 1 ) (a-P 2 ) where the initial ray direction is given by the polar angle and azimuthal angle q5 and the ray inter- sections with the surfaces occur at X, Y, Z and X2, Y 2 , Z and Z1 = f( + Al); Z2 = f(1 - A2); A,,A2 0- The telescope focal length, f, is defined as the distance from the focal plane to the plane formed by the central edges of the parabolas. The exact solutions are: April 1971 / Vol. 10, No. 4 / APPLIED OPTICS 945
Transcript
Orthogonal Mirror Telescopes for X-ray Astronomy
L. P. VanSpeybroeck, R. C. Chase, and T. F. Zehnpfennig
Crossed mirror telescopes are presented as an alternative to the present telescope systems used in x-rayastronomy. These instruments generally have a higher x-ray collecting efficiency but a poorer angularresolution than the more conventional paraboloid-hyperboloid telescopes. They also can be made moreeasily and quickly as was demonstrated by a recent rocket flight that used a simplified mirror design withonly one-dimensional focusing.
The application of focusing x-ray optics to x-rayastronomy was first discussed by Giacconi and Rossi.'Since that time much work has been done on grazingincidence imaging systems. The most commonlyused system consists of two successive conic sectionsof revolution.', 3 Telescopes of this geometry havebeen used with great success for obtaining high resolu-tion photographs of the sun in x-rays. 4' Fisher andMeyerott 6 have built another type of system with one-dimensional focusing which is composed of reflectingparabolas of translation. A system of one-dimensionalfocusing has recently been flown successfully in asounding rocket by Gorenstein et al.7 ; during thisflight x-ray images of the Cygnus Loop were obtained.As an alternative to the present instruments, we havedesigned several telescope configurations that focusthe x rays with sets of two orthogonal parabolas oftranslation. The use of crossed mirrors for x-rayfocusing was first proposed by Kirkpatrick and Baez."McGee successfully demonstrated the use of crossed-spherical reflectors in an x-ray microscope.9
A simplified Kirkpatrick-Baez device is shown inFig. 1(A). The incident ray successively strikes twoparabolas at approximately right angles to each other.In practical designs, the surface area is increased byusing many approximately parallel parabolas as inFig. 1(B).
All authors were with American Science and Engineering,Cambridge, Massachusetts 02142, when this work was done;T. F. Zehnpfennig is now with Visidyne, Inc., Woburn, Mas-sachusetts 01801.
Received 18 September 1970.
The equations for the individual surfaces can bewritten:
= pi' + 2Pl(Zl + a),
Y2 = P,' + 2P2Z2,
Y, arbitrary, (1)
X2 arbitrary, (2)
where Z is the symmetry axis, the focal plane is at Z =0, and the x rays first strike the surface described byEq. (1). P1, P2, and a are constant parameters. Thedisplacement of the focus of the first parabola is neces-sary because of the second reflection, and optimum focusis achieved when a = P2 . This condition cannotbe exactly achieved if many approximately parallelsurfaces are used to reflect in the Y-Z plane since suchsurfaces necessarily have different values of P2. Inthis case we set a equal to the average value of P2.
If a P, the resolution is primarily determinedby the length of the mirror segments; neglectingall correction small compared to the effects determinedby the length of the mirror section, we obtained thefollowing approximate (see next paragraph) intersectionof a ray in the focal plane:
yF = f(l - A) tanG sin+,
YF = f(l + Al) tanG sinj ± f (X1) (a-P 2 )
where the initial ray direction is given by the polarangle and azimuthal angle q5 and the ray inter-sections with the surfaces occur at X, Y, Z and X2,Y2, Z and
Z1 = f( + Al); Z2 = f(1 - A2); A,,A2 0-
The telescope focal length, f, is defined as the distancefrom the focal plane to the plane formed by the centraledges of the parabolas.
Fig. 1. (A) A simple Kirkpatrick-Baez device. (B) A nested set of orthogonal mirrors. (C) A representation of the front aperture of the
telescope with rectangular geometry. The focal length of this telescope is 559 cm. am. = 2.60. The depth of each set is 50.8 cm. The
thickness of the mirrors is 0.635 cm. (D) A representation of the front aperture of the telescope with sixteenfold symmetry. The focal
length is 792.5 cm. ma,. = 1.250. The depth of each of the two sets of orthogonal parabolas is 61.0 cm. The mirror thickness is 0.317cm. Each module is encased in a container 0.635 cm thick and has 51 mirrors; 26 in the front set and 25 in the rear set.
X tanG cos + (z a) ( - P2) + ( + )z z+ ±I P2 (1 2(1+zla)(zxl ) ( Y'P2 ) tan sing
+ a z, + a zz + P++(+ a -P2 + Pl) Y..2) r , ) l82 (Z2 - Z)
Z + P2 \Z2J Lz + a} z + a
X tan2G sink coso }
*+ +± za tan cos) I + + tanG coso
+ ( i ' ) tan sing)}-
The radius of the blur circle for a symmetric geometryis thus proportional to (Amax) which is the length of themirror segment over the focal length. Therefore,this quantity should be minimized to obtain highresolution. To cover an aperture one is thereforetempted to use many short mirrors rather than onelong mirror. However, because the mirrors have afinite thickness, this will sacrifice collecting area.Thus, for a given application a compromise betweencollecting area and resolution is required.
The approximate grazing angle of axial rays incidenton the first surface is given by a = 21arc tan(x,/f),where x is the central distance from the axis to thissurface. Similarly, the approximate grazing angle ofaxial rays on the second surface is a = arc tan ye/f.
When a exceeds the critical angle for the givenwavelength and material, mirror reflection efficiencydrops off very rapidly. Consequently, there is aneffective upper limit to allowable values of the telescopediameter divided by the focal length. In general,the critical angle increases with increasing wavelengthand atomic number and density of the material. Inmost cases the spacecraft envelope determines thetelescope focal length. The aperture is then limitedby the maximum grazing angle consistent with thedesired short wavelength response. If the primaryexperimental objective is to search for faint objects,one wishes to maximize the collecting area. This inturn will dictate that fewer but longer mirrors should beused to cover the entire available aperture. If, onthe other hand, the experimental objective is to make adetailed study of objects of approximately known inten-sity, one will usually choose the best possible resolutionconsistent with the necessary sensitivity.
In one of our designs we arranged parallel sets ofmirrors into four rectangular modules. The appear-ance of the modules at the front aperture is shown inFig. 1(C). The motivation behind this design was adesire to maximize the collecting area for a survey
mission. Each module consists of 22 parabolic sheetsfollowed by 26 sheets at right angles to the first.We analyzed the performance of this telescope with aray-tracing computer program. Fixed angle raysarriving at random locations in the front aperture weretraced through the system in a Monte Carlo process.The surface reflection efficiency as a function of wave-length and grazing angle was taken into accountusing the formalism presented in Ref. 2, pages 12-14.Rays which hit the backs or edges of mirrors wererejected. The reflecting surface was assumed to bechromium.
We define the effective collecting area of the tele-scope as
Aff = Ageom (-V) (Ziei 2 )
where the sum includes only the rays that reach thefocal plane, el and Ei2 are the reflection efficienciesfor reflection from the first and second parabola,respectively; Ageom is the geometric area that raysmay traverse at the front aperture; and N is thenumber of random rays incident on the front aperture.
In Fig. 2, we have plotted the effective collectingarea vs wavelength for various angles of incidence.The dip at about 21 A is due to the L absorption edgesof chromium. The points of this figure and of thefigures that follow were calculated to approximately5% accuracy. In Fig. 2 the azimuthal angle, , ofincident rays were fixed at zero degrees ( measuredfrom the x axis). At 4 = 900, the effective area isappreciably larger for large . For 40-A rays and4 = 90°, Aff = 1097 cm2 at 0 = 20', and Aff = 555cm2 at = 1.
to
10'
tb
A.
tS
10ICo"WAVELENGTH (Ad)
10'
Fig. 2. Effective collecting area of the telescope with rectangulargeometry vs incident wavelength. Results are given for severalvalues of the incident polar angle 0. The azimuthal angle of
incident rays is fixed.
April 1971 Vol. 10, No. 4 / APPLIED OPTICS 947
02
l 11 1 I I I I I I I I I I I
_ , , , Jo,,, ,, , . 1 , . . .
AX .AS .-
I I I I I I I I I I . I . - I I L
Some of the rays that reach the focal plane arereflected only once from either a front or a rear mirror.Others reach the focal plane undeflected. These back-ground rays can easily be distinguished from raysthat make two reflections because, in general, theywill reach the focal plane at locations other than theimage location of two reflections. They can also beeliminated by an appropriate collimator at the front,aperture.
In Fig. 3 we have plotted the rms blur circleradius on a flat focal plane vs polar angle of incidence.The blur circle radius is not appreciably dependentupon the azimuthal angle of incidence of the rays.
An alternative Kirkpatrick-Baez telescope configura-tion is shown in Fig. 1(D). This design had a definiteresolution goal of 30 sec of arc determined by an asso-ciated crystal spectrometer. The required resolutionfixed the mirror depth and thickness. Subject tothese constraints and the constraint of the envelopeconfiguration we wished to maximize collecting areain the wavelength region greater than 3 A. Figures4 and 5 are, respectively, the effective area and theresolution results for this design. The surface materialis nickel, and the dip corresponds to the L edges ofnickel. This type of design, of course, has negligibleazimuthal dependence.
Telescopes of the crossed parabola design cangenerally be fabricated more easily and quickly thanparaboloid-hyperboloid types of comparable x-raygathering capacity. Because the mirrors need not beself-supporting during polishing or over large spansin the final instrument, they can be made quite thin,and this in turn makes very efficient use of the availablefront aperture. The use of optical flats assures thebest possible surface finish available and thereforethe highest reflection efficiencies. Experiments canbe precisely tailored to their objectives because thetelescopes are easily made. For example, a telescopeof large grazing angle would be used for soft x-raysources, whereas a smaller grazing angle instrumentwould be used to detect the hard portion of the spectra.
A simple two-mirror crossed parabola telescope hasbeen made and tested in our laboratory. The mirrorswere made of polished glass and measured 0.25 cm X20.3 cm X 20.3 cm deep. They were each positionedabout 5.7 cm from the optical axis and were con-strained to an approximate parabolic shape by clampsat three points on each side. The focal length wa~s190 cm. A clear x-ray focus was achieved at 7.0 Awith a resolution of about 35 sec of arc. The imageprofile indicates that the resolution was limited byincorrect curvature rather than by microscopic imper-fections in the surface.
The sounding rocket flight of Gorenstein et al.7
demonstrates that multiple parabolas of translations,such as have been proposed here, can be successfullyfabricated. The telescope used on this rocket consistedof eight plates of 0.10 cm thick chromium platedcommercial float glass backed by 0.051 cm of steel.Each plate was 18.8 cm X 40.6 cm and was con-strained to the calculated parabola by a series of
I40 - _ - l__
I_ . I . . -
0 20 30 40 50 60 70 80 90 M00OIOOC MIN
Fig. 3. The rms blur circle radius of the telescope with rec-tangular geometry vs incident polar angle.
accurately located pins. The theoretical reflectivity,calculated by the same program which yielded Figs.2 through 5, was verified at 9.87 A to within about20% by laboratory measurements. The resolution,however, was considerably worse than calculated as aresult of ripples in the glass.
In conclusion, the crossed parabola systems shouldfind application in astronomical observations such ashigh sensitivity surveys, photometry, and certain kindsof spectroscopy where a large effective area rather thanhigh angular resolution is the most important factor.
R. Giacconi, H. Gursky, P. Gorenstein, G. S. Vaiana,and many other individuals at American Science andEngineering contributed to the experimental configura-tions discussed in this paper. The work reported herehas been done in part under NASA Contract NAS8-24385.
104 I I IL
l: 10 801=~~~~~~~~~~~~~~~~,
Li.
t 10 0'A 0 t
WAVELENGTH (A )
Fig. 4. The effective area of the telescope with sixteenfoldsymmetry vs incident wavelength for various polar angles.
948 APPLIED OPTICS / Vol. 10, No. 4 / April 1971
,00-
-60
I
20 -
30L
20L/
10-
2 4 6 8 10 12 14 166(ARC MIN)
Fig. 5. The rms blur circle radius of the telescope with sixteen-fold symmetry vs incident polar angle.
References1. R. Giacconi and B. Rossi, J. Geophys. Res. 65, 773 (1960).2. R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. VanSpeybroeck,
and T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
3. J. D. Magnus and J. H. Underwood, Appl. Opt. 8, 95 (1969).
4. G. S. Vaiana, W. P. Reidy, T. Zehnipfennig, L. VanSpey-broeck, and R. Giacconi, Science 161, 564 (1968).
5. L. P. VanSpeybroeck, A. S. Krieger, and G. S. Vaiana, Nature227, 818 (1970).
6. P. C. Fisher and A. J. Meyerott, IEEE Trans. Nucl. Sci.NS-13, 580 (1966).
7. P. Gorenstein et al., "Soft X-Ray Observation of the CygnusLoop," presented to the 14th International AstronomicalUnion General Assembly, Brighton, 1970 (to be published inScience).
8. P. Kirkpatrick and A. V. Baez, J. Opt. Soc. Amer. 38, 766(1948).
9. J. F. McGee in X-ray Microscopy and Microradiography,V. E. Cosslett, A. Engstrom, and H. H. Patte, Eds. (AcademicPress, New York, 1957), p. 164.
Symposium onVisual Performance when Using Optical Instruments
21-23 July 1971 Munich
The German Optical Committee, supported by the International Commission forOptics, will organize this symposium next July in Munich, to be held under theauspices of the German Society for Applied Optics. Three hundred participantsare anticipated. Papers, which may be given in English, French, or German, willdeal with the interactions between eye and optical instrument, with emphasison any improvements or modifications of the visual performance due to theoptical instrument as well as on particulars of the visual system to be consideredin the construction and use of optical instruments. It is planned to have invitedand contributed papers presented on the following groups of topics: (1) Physio-logy of the visual system, especially latest research in retinal perception charac-teristics, including the Stiles-Crawford effect; wavelength and frequency filter-ing; color perception; recognition of motion and binocular perception; and theextent to which these characteristics are affected by the interaction of eye/opticalinstrument. (2) Improvement of visual perception through use of magnifyingoptical instruments while maintaining control over the resulting deterioration ofsuch other visual functions as field of view and photometric contrast. (3) Influ-ence of the visual functions when using subjective optical measuring instru-ments: (a) instruments for measuring direction and distance in physical space(measuring telescopes, direction finders, rangefinders); (b) instruments formeasuring light or color (photometers, clorimeters, pyrometers, etc.); (c) otheroptical measuring instruments. (4) Effect of eyeglasses and contact lenses onthe various visual performance characteristics. (5) Changes in the visual per-formance when using image converters, image intensifiers, or display screens.(6) Extent of the worsening in visual performance due to relative motion of ob-server and instrument. Further information can be obtained from the chairmanof the symposium, Herbert Schober, Institut fr medizinische Optik der Uni-
