JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Reflecting Objective for Microspectroscopy*

WAYNE THORNBURGtPhysico-Cliemical Biology Department, University of Illinois, Urbana, Illinois

(Received March 25, 1955)

Interest in the low-temperature ultraviolet absorption spectra of biological materials has led to the designand construction of a reflecting microscope objective in which the conventional, two-element system ismodified by the addition of a reflecting correction plate. The system has high aperture, low central obstruc-tion, long working distance, and zero chromatic aberration. The correction plate simplifies certain problemsin construction and eliminates the need for figuring surfaces with deep curvatures.

INTRODUCTION

THE techniques of low-temperature spectroscopyhave been employed in biochemical studies'

and the possible application of these methods to cyto-chemical problems have been considered. Severalspecial problems arise in low-temperature micro-spectroscopy. Microscope objectives with workingdistances of the order of 1 cm are required for adequatethermal isolation of optical elements and the specimen.High aperture and excellent spherical correction arenecessary for adequate resolution of cellular com-ponents. In order to realize the increased resolution ofabsorption bands which can be obtained at low tem-peratures, the optical system must be quite free ofchromatic error. Mounting of the specimen is a seriousproblem. Some means for avoiding the accumulationof frost on the specimen is also necessary. Finally, thesystem should work with high efficiency in the near-ultraviolet region, this usually being the one of greatestinterest.

In many respects some of the reflecting objectivesdeveloped by Burch' provide an ideal solution to theseproblems. Such equipment was not available, however,and it seemed likely that the modification of anyexisting equipment for low-temperature work wouldbecome a major problem in itself. Moreover, the prep-

Reflecting Condenser,

''- Reflecting Objective

FIG. 1. Schematic view of optical system.

* Submitted in partial fulfillment of the requirements for thedegree of Doctor of Philosophy in physico-chemical biology.

t Present address: Anatomy Department, University of Wash-ington, Seattle 5, Washington.

I G. I. Lavin and J. N. Northrop, J. Am. Chem. Soc. 57, 874(1935).

2 Scott, Sinsheimer, and Loofbourow, Science 107, 302 (1948).3 C. R. Burch, Proc. Phys. Soc. (London) 59, 47 (1947).

aration and centration of aspheric surfaces of largecurvature have proved to be very difficult problems.For these reasons an alternative solution was soughtamong optical arrangements involving three and fourfirst-surface mirrors. It was important that any alterna-tive solution be constructable with moderate amountsof skill and money. The reflecting objective describedbelow is a result of these efforts. It employs a thirdreflecting element which is referred to here as a re-flecting correction plate. This objective has been builtand incorporated into a low-temperature microspectro-graph.

DESIGN OF OBJECTIVE

The image-forming errors of a concave, sphericalmirror can be partly corrected with a smaller, convex,spherical mirror. With a proper choice of parameters,known as the "Schwartzschild aplanat condition,"4

and low aperture this correction is extremely good. Athigher apertures the image deteriorates, somewhat.The diagram of the condenser in Fig. 1 illustrates thegeneral features of this combination. Further correctionmay be achieved by making either or both of thesesurfaces aspheric or by employing additional surfaceswhich, in turn, may be spherical or aspheric. Whilemany of the possible combinations of three or morereflecting elements show some promise from an opticalpoint of view, most of them are ruled out because theydemand impossible locations of specimen, condenser,supports, etc.

One arrangement was discovered in which the addi-tion of a flat mirror had the effect of replacing the con-cave mirror by its image. The diagram of the objectivein Fig. 1 illustrates this arrangement. While only threeoptical surfaces are involved it behaves like a four-element system, each ray being reflected twice from theflat surface. Designs for the objective depend upon thefact that slight deviations from flatness in this addi-tional surface may be used to correct residual sphericalaberration. In this sense it becomes a reflecting cor-rection plate and resembles the refracting elementin the Schmidt camera.

At the beginning of this work attempts were made toderive an analytic solution for the correction plate but

I C. R. Burch, Proc. Phys. Soc. (London) 59, 41 (1947).

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VOLUME 45, NUMBER 9 SEPTEMBER, 1955

September1955 REFLECTING OBJECTIVE FOR MICROSPECTROSCOPY

these were abandoned because of the difficulty in im-posing proper conditions upon the equations and thegeneral awkwardness of the expressions which arose.It was clear that a surface did exist which would com-

pletely eliminate spherical aberration. Later it appearedthat a family of these surfaces existed, each associatedwith a slightly different position of the correction plate.It remained to select the best type of surface from thefamily and to specify it as accurately as possible byapproximate methods.

If possible, three other conditions should be met.First, and most important, that part of the aperturewhich is obstructed by the convex mirror should bekept small. From the work of Dunham,' it is concludedthat the diameter of the central stop should not begreater than 0.35 the diameter of the aperture. Largervalues result in a deterioration in the image. A similarconclusion is reached by Norris and Seeds.6 Next, inorder to simplify the figuring and testing routine, thecorrection plate should not contain zones of flexure.Finally, the correction plate is more easily mounted ifit is concave, its outer edge being left undisturbedduring grinding and polishing. Any additional freedomshould be used to minimize the offense against the sine

condition. It was found that these three conditionscould be met simultaneously. Some freedom remained in

the choice of the radii of the two spherical surfaces.Calculations on the system were made by ray tracing.

Refinement of the various parameters at each stage wasbased on interpolation and intuition. The correctionplate was first approximated by a spherical surface,then by a cone, and finally by a hyperbola of revolution.The hyperbola was quite successful and produced resultsclose to those of the required surface. This result,together with certain theorems from projective geom-etry encouraged further attempts to deduce an analyticsolution by applying the focal properties of a hyperbola.However, it was later decided that the hyperbola wasonly an approximation and that an exact solution wouldinvolve an equation of at least the fourth order. Thebest set of parameters obtained appears in Fig. 2.

The hyperbola deviates from the required surface byseveral fringes, the exact amount being unknown.Further refinement of these calculations could have beenmade but at the time it was not considered economic.According to the construction plan, the figure of thecorrection plate was to be determined by testing thiselement in the assembled objective. The approximatesolution was adequate for preliminary grinding andpolishing. Also, it was not clear that the solution couldbe much improved without going to a more complicatedcurve.

5 T. Dunham, Jr., "The effect of central stops on the resolutionof a microscope, I," Special Rept. No. 2 to the American CancerSociety (July, 1948).

6 Norris, Seeds, and Wilkins, J. Opt. Soc. Am. 41, 111 (1951.)

FIG. 2. Plot of optical parameters.

L,-50.0 cm D2 -1.00 cmL 2 - 4.750 cm D 3 -0.916 cmL3- 2.825 cm D4 -2.10 cmL 4 - 1.168 cm R1 -4.000 cmDI- 6.93 cm R 2 -0.788 cm

Hyperbola: 5000X 2= Y2 +2 cm. Asymptotes: 890 11k'. Depth atcenter: 0.0334 cm. Maximum aperture, 2 angle: 500. Obstructedaperture, t angle: 15°. Obstruction ratio: 0.34. Focal length:0.5 cm. Nominal working distance: 0.75 cm. Magnification: 100.Numerical aperture: 0.77 dry.

CONSTRUCTION OF OBJECTIVE

Spherical surfaces for the reflecting objective werepurchased from an optical supply house. The correctionplate was ground from a flat blank by hand. The firststep was to prepare a concave spherical surface whichwas tangent to the required hyperboloid at its outeredges. Then, by using progressively smaller grindingtools the inner zones of the hyperboloid were ap-proached. A series of pitch polishers were used in asimilar fashion to obtain the final figure. In preliminaryoptical tests the radii of curvature of various zoneswere compared with those of the required hyperboloid.Final tests were made by assembling the objective andusing a modification of the Foucault method to examinean artificial star.

Details of the low-temperature microscope are shownin a sectional view in Fig. 3. The small, convex mirror of

the objective, No. 3, is cemented to an Invar steeltripod which rests directly on the surface of the concavemirror. The correction plate, No. 1, is in contact withthe edge of the large mirror and is held in place by

light pressure from above. Immediately beneath theobjective is a specimen holder which is made of fusedquartz and provides for the circulation of liquid ni-trogen. The condenser matches the objective in aper-ture but is not as well corrected. The entire chamber issealed with gaskets and bellows in order to permitthe elimination of water vapor. Water jackets providefor thermal isolation of the specimen holder by holdingmetal supports at room temperature.

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WAYNE THORNBURG Vol. 45

DISCUSSION

There are obvious arguments against an opticaldesign in which all surfaces are not completely speci-fied. One of these is that exact prediction of other errorsin image formation is not possible. If necessary, thesecalculations could be refined and this difficulty avoidedwith the help of modern computing methods. It is adesign in which microscope manufacturers are not aptto be interested on account of the aspheric surface.However, for special applications and for the builderwith limited facilities this objective has some points inits favor.

Like other systems which do not contain refractingelements the useful spectral range of this objective islimited only by the reflectivity of its surfaces. Thefiguring routine which has been used to remove sphericalaberration is largely a matter of convenience. The taskis comparable in difficulty with the preparation of aparabolic reflector for the small telescopes which havebeen built by many amateur astronomers. It avoids theproblem of figuring the deep curvatures which arecharacteristic of the two-element systems. In this casethe correction plate was nearly flat, asymptotes to thecurve deviating from a flat surface by about 48 min.

- I !

It simplifies final testing because the correction platecan be removed and replaced without disturbing thelocation of other elements. The glass-to-glass contactwhich determines the spacing of elements was usefulin this respect. Finally, the centration problem isminimized. In the two-element aspheric systems thesurfaces must be accurately positioned with respect tothree translation and two rotation axes. With this designthree translations are required to locate the sphericalmirrors. Errors in the axial direction are automaticallycorrected in preparing the correction plate. Slighterrors in the other two directions are well compensatedby relatively large lateral motion of the plate on itsglass mounting surface.

In principle it should be possible to polish one surfaceas accurately as another. It is felt, however, that thisdesign may permit a technical advance in the precisionwith which reflecting objectives may be figured. Asmore rigorous demands are placed upon the construc-tion of these objectives (such as their possible use ininterference microscopes or their application to stillshorter wavelengths vacuum ultraviolet region wouldimply) the correction plate principle may acquire amore direct importance.

FIG. 3. Sectional view of low-temperature microscope. 1. Correction plate. 2. Concave mirror of microscopeobjective. 3. Convex mirror of microscope objective. 4. Invar steel tripod. 5. Top of low-temperature stage.6. Water jacket for thermostating objective supports. 7. Rubber bellows, sealing stage to microscope chamber.8. Water jacket for thermostating stage support. 9. Stage clamping screw and rubber seal. 10. Convex mirror ofcondenser. 11. Concave mirror of condenser. 12. Rubber diaphragm. 13. Condenser aperture stop.

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September1955 REFLECTING OBJECTIVE

Immersion objectives are not practical for low-temperature work. For other applications an hemi-spheric immersion element could be added to thisobjective without otherwise modifying the design. Withfused quartz the numerical aperture would be increasedto about 1.25. An immersion element could also supportthe convex mirror, as has been done in previous designs.Such an objective should be quite stable, both me-chanically and thermally, since its assembly would de-pend entirely on glass-to-glass contact.

The performance of a model of this objective wasquite satisfactory. The resolution was somewhat lessthan the theoretical value (0.8 of the wavelength)because at the time the objective was put into use thespherical aberration had not been completely removed.From an examination of microcrystals, the actual re-solving power appeared to be about 0.6 /, at all wave-lengths. In microspectroscopy large object fields areconvenient but they are not usually considered to beessential. Calculations indicated that the diameter ofthe comatic circle would be about 4.0% of the distancefrom the axis. Actual performance appeared to be an

improvement over this prediction. At its practicalresolution the usable field was approximately 100 in diameter. Subsequent calculations indicate7 that theoffense against the sine condition can be reduced withsomewhat deeper hyperboloids. The 0.75-cm workingdistance made possible the use of a liquid air stage.The equipment has been used successfully in the studyof the low-temperature absorption spectra of micro-crystals and of samples of biological material downto 1 sq A in area.

ACKNOWLEDGMENTS

The author wishes to thank Dr. G. M. Almy and Dr.R. D. Rawcliffe for their advice and support of thisproject. Mr. D. Sipult's excellent machine work on themicroscope is greatly appreciated. Construction ofthe microspectrograph was made possible by a grantfrom the Graduate School of the University of Illinois.

7 Further work is in progress on the design of optical systemsfor low-temperature microspectroscopy. It will be reported whentests on a second reflecting objective are complete.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 45, NUMBER 9 SEPTEMBER, 1955

Some New Formulas for Determining the Optical Constants from Measurementson Reflected Light

R. W. DITCHBURNPhysics Department, Reading University, Reading, England

(Received September 28, 1953)

The theory of reflection at the surfaces of metals and semiconductors (with special reference to the latter)

is considered.Convenient equations for calculating the real and imaginary parts of n' (a is the complex index) from

measurements of A (the phase difference) and zp (tan/ = a'= the ratio of the two reflection coefficients) for one

angle of incidence are derived. A second set of equations for calculating the optical constants when either

ip or A have been measured at two angles of incidence are given. The errors are analyzed to show which

method is most sensitive when the constants are in certain ranges. Difficulties caused by inhomogeneity near

the surface and by surface films are discussed, and possible methods of elimination are suggested.

1. INTRODUCTION

THE amount and ellipticity of the light reflectedT by the surface of an absorbing medium maydepend on (a) the optical constants of the bulk material,(b) the special properties of a surface layer producedby polishing, and (c) the properties of an overlyingsurface film, e.g., a film of oxide or of adsorbed gas on ametal. The ellipticity is very sensitive to (b) and (c) sothat, under favorable conditions, a film 2 A thick canbe detected. This sensitivity is advantageous when onewishes to detect a monomolecular film but it sometimesmakes the interpretation of experimental results verydifficult. Most work on absorbing media has been donewith metals. The present discussion relates more directlyto certain types of semiconductors. These substancespossess an absorption edge at some wavelength Xe, the

absorption coefficient being high on the short-wave sideof Xe. The order of magnitude of quantities may beshown by stating some values for amorphous selenium.' 2Let n= n-ik be the "complex index," where k/nis the extinction coefficient. The absorption coefficientca= 4rk/X. For amorphous selenium the absorptionedge at room temperature is at about 0.75yu. At about2.Opt the absorption coefficient is <1.0 cm'l and k is

very small, i.e., the material is nearly as transparent asoptical glass. At O.4 A the absorption coefficient isabout 2.5X 105 cm-l, i.e., k= 1 (approx). This value iscomparable with, but somewhat smaller than, the valuenormally obtained for a metal (k about 3).

1 M. A. Gilleo, J. Chem. Phys. 19, 1291 (1951).2 H. A. Gebbie and E. W. Saker, Proc. Phys. Soc. (London)

B64, 360 (1951).

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