Multiply Diffracted Light in the Czerny-Turner Spectrometer

Joshua J. Mitteldorf and Donald 0. Landon

At certain small angles of the grating, any in-plane spectrometer will pass stray light that has been C-turned by the reflecting optics for a second diffraction. Paths of this source of stray light and its strue-ture have been calculated and confirmed experimentally.

1. Introduction

The possibility of multiply diffracted light reachingthe exit slit is inherent in the design of all in-plane (e.g.,Littrow, Ebert, Czerny-Turner) spectrometers. Forany given design, there are discrete ranges of gratingsettings at which multiple diffraction paths are realized.Because the resulting spurious radiation arrives de-focused at the exit slit, a broad but well-defined bandof wavelengths may be detected at an intensity typicallytwo to three orders of magnitude below that attained atthe primary grating setting for these wavelengths.Unlike grating ghosts, multiply diffracted bands bearno direct linear relationship to the wavelength settingof the instrument; their positions are, nevertheless,predictable and with proper precautions they can beeliminated.

11. Qualitative Study

Figure 1 is a schematic of a Spex model 1700 4-

meter Czerny-Turner Spectrometer for which doublediffraction bands have been calculated. The mainsource of multiply diffracted light at low wavelengthsettings is specular reflection of once-diffracted lightthat has been focused back on the grating by eithermirror (Fig. 2). The position of both mirrors is suchthat their respective foci are approximately halfwaybetween either slit and the grating; thus, light from thegrating is reflected by either mirror along a line nearlyparallel to the central axis of the instrument. Specularreflection to the focusing mirror must take place at theangle 0o (Fig. 1) for the stray light to reach the exit slit.Therefore, a peak in stray light is predicted for 6 = 0o, corresponding to a wavelength setting of 1980 A with

a 600-lines/mm grating. In fact, scanning the instru-ment through the uv with an incandescent source of

J. J. Mitteldorf is at Harvard College, Cambridge Massachu-setts 02138; D. . Landon is with Spex Industries, Inc., Me-tuchen, New Jersey 08840.

Received 1 February 1968.

visible light reveals a broad baud of stray light peakingat the 1980-A setting.

Since the doubly diffracted visible light arrives out offocus at the exit slit, determining its structure explicitlynecessitates tracing individual rays of light through theoptics. Each path can be assigned two parameters andplotted on a artesian plane. Physical limits of theoptical components then limit scattering to two tri-angular regions of the plane of paths (Fig. 3). The twograting equations (one for each diffraction) determine Xfor each path represented in the plane; equating thewavelength values determines a line in the plane.Finally, the intersection of this line with the triangularregions will represent all possible paths for stray light,and either grating equation determines X for pointsalong the segment of intersection. In this manner, thewavelength range of stray light passed at a givenmonochromator setting will be computed.

111. Quantitative TreatmentA beam of parallel rays illuminates the width of the

grating from which a diffracted ray may leave any pointat a continuous range of angles. From here the wave-length and future path of a given ray are determined bythe geometry of the system. It is clear, then, that twoindependent parameters are required to specify a par-ticular ray of light. Choose as the two parameters 0,the angle (measured from the central axis) at which theray emerges from the grating in its first diffraction, andy, the distance from the axis at which the ray strikeseither mirror after its first diffraction (Fig. 2). Bothwill be called positive above the central axis. Theneach possible path for a ray of light corresponds to apoint on the y-+o Cartesian plane. This choice of para-meters permits the representation of the angle of inci-dence for the second diffraction, again measured fromthe central axis, as

- [y/(F costo)] i4- ±o - [A/(F cos4)o)l (1)+ if once-diffracted light strikes collimating mirror (Path A)- if once-diffracted light strikes focusing mirror (Path B),

which is a simple linear function of f and y, so bothgrating equations take o a manageable form. Fur-

August 1968 / Vol. 7, No. 8 / APPLIED OPTICS 1431

Fig. 1. Selmenatic (of the Spex Czerny-Turner monochromator with principal ray traced. A1 = 76 mm, B = 24 mm, C = 126 mm,E = 635 mm, F = 748 mm, V = 102 mm, O = 0.1176 rad (6O44'10u').

EXITSLIT D … --- - -F

GRATING _--- --

_CENTRALI-

DI _ SPU ROUSRAY. E _-__ RI _ _ _ CENTRANCE - SPURIOUS RAY A -. I-SLIT I

ICUSINGI RROR

_YA

DLLIMATINGIRROR

Iig. 2. Schernati with two double diffraction paths. Ray A reflected twice fom the collimating mirror; ray B reflected twice fromthe focusing mirror. Note definitions of y and .

I l ermore, the effect of the physical limits of the opticalsurfaces may be expressed i a form independent of 0.Thie faet that the light leaves the grating of width Wat a angle a strikes a mirror at a distance E at apoint I/ from the central axis is expressed in the in-equlality:

-- lW I+ Btlno4 < y < + w + E tan.

Siiice t he angle is small, a linear approximation mayibe sbstitiited, facilitating later calculations:

--4 + E) < < + w + E. (2)

(All fuLlture equations will be written i this form withsmall angles approximating their sines and tangents,cosines set = 1.)

The point y where the ray arrives at the right-hand(lid of the instrumeiit must be on one of the mirrors:

- C < <-B (3a)

,i

B < < C. (3b)

Finally, light leaving the mirror from a point y at anangle given by Eq. (1) must arrive at the grating sur-face E mm away between - v and + w:

_ _ _ A-21?v < ?/ + E 0 0FCS 0 +(° FCO2o (F cosloo F cosl4oj

< +2w, (4n)

-v < ?J + E [-F cos4o -(0 - F'°s44)l

< +2w. (4b)

The above inequalities define two triangular regionsof the y-O plane in which the geometrical limits of theoptical components permit doubly diffracted light toreach the exit slit (Fig. 3). Area A corresponds to lightstriking the collimating mirror after its first diffractionand returning to the grating; area B corresponds tolight returned by the focusing mirror for the seconddiffraction (Fig. 2, paths A and B). In an Ebert sys-tem, where a single continuous mirror replaces thetwo separate Czerny-Turner mirrors, the region is coii-nected, and its boundary is a parallelogram. Ofcourse, most, Ebert spectrometers use mirror masks so

1432 APPLIED OPTICS / Vol. 7, No. 8 / August 1968

that the actual behavior is not distinguishable fromthat of the Czerny-Turner.

Two grating equations, one for each diffraction,determine X as a function of a point in the y-O plane:

nX = d[(O + Oo) + (0 - )], (5)

mX = d + - + 'Po )]F coso+ F cos4o)]

+ [0- ol0} (6a)

mX = d L0 + - cos44o - 0 - cos 24o)]Fos o F coslo

+ [O-)ol } (6b)

Here, n = the order of the first diffraction, m = theorder of the second diffraction, d = spacing of gratinglines, 0o = 0.1176 (see Fig. 1), = (see Fig. 1) gratingsetting = Xo/2d cos40 for a wavelength counter readingof Xo, and F = focal length of mirrors (see Fig. 1) = 748mm.

For any given ratio n: n, X may be eliminated fromthe two Eqs. (5) and (6), leaving a linear equation in yand A, a line in the cartesian plane. Combinations ofy-k values leading to double diffraction scattering occurat points along this line that also lie within the appro-priate shaded region of the plane. The problem ofpredicting scattering has been reduced to substitutingvalues of 0, n, and m into Eqs. (5) and (6) to find linesthat intersect the shaded triangles. The explicitcalculations are reproduced here for d = 16,667 A (600lines/mm). Values of other parameters for the Spexinstrument are as in Fig. 1.

IV. ApplicationFor monochromator settings in the uv with a 600-

lines/mm grating longer wavelengths ae passed onlyfor m = 0. Equation (6) becomes an equation in y and0 when values of 0, corresponding to counter settingsof o = 2d6 cosoo, are substituted. In Fig. 3, two ofthe relevant lines are plotted. The line derived fromEq. (6a) and corresponding to Xo = 1980 A intersectsthe shaded region A along the segment from (-49,-0.083) to (-24, -0.052). Substituting these valuesback into Eq. (5) with n = 1 yields a range for X from4780 A to 5340 A, i.e., with the instrument's counter set,at 1980 A, 4780-5340 A will be reflected and twicediffracted to the exit slit. Similarly, Eq. (6b) has beensolved at Xo = 2900 A, yielding a line through area B ofFig. 3. Substituting values of X at the endpoints intoEq. (5) reveals that the segment corresponds to =3630-5060 A.

Once the orders of diffraction are known, the equa-tions may be combined algebraically, eliminating thegraphic process. Solving Eq. (6a) simultaneously witlEq. (3a) and (4a) yields, respectively, an upper and alower limit for 0 which, in turn, may be substituted intoEq. (5) to give a lower and upper limit for N. Sinceall the above equations are linear, they combine simpleto yield another linear equation. For n = 0, n = 1,spurious path A,

2.01X5 + 780 A < X < 1.16X0 + 3050 A. (7a)

Once again, No is the counter setting and X is the wave-length of scattered light. The upper limit will begreater than the lower limit for Xo < 2640 A, showingthat for these values the line intersects the shadedtriangle (Fig. 3) and double diffraction scattering canoccur.

Repeating the calculation for Eq. (6b) combined wit hEqs. (2), (3b), and (4b) yields:

Fig. 3. The y-o Cartesian plane. Shaded areas contain points corresponding to paths of type A and B, respectively, in Fig. 2, Linesegments (6a) and (6b) are each derived from two simultaneous grating equations.

August 1968 / Vol. 7, No. 8 / APPLIED OPTICS 1433

7000 A

6000A

5000 A

4000A 3ooA i - -

3000 A

2000 A

1OOOA

1000 A 2000 A

Fig. 4I. Wavelength range of stray light (shafunction of monochromator setting. Only straifrom double diffract ion in the first and zeroth orde

ford. = 0, t, = 1, Spur-iOUS pat II 13,

above 3160 A: 7.67N, - 20:300 Xhelow :3160 A: L.16Xo + 270 , <

predicting scattering for 1230 i < No < 341These results are concisely summarize(

which wavelength of scattered light () ifunction of monochromator setting (X0).

V. Experimental

tions, triple diffraction scattering can occur only at avery few widely separated grating settings.

oe For No = 2300 A, Eqs. (7a) and (7b) predict bands at5420-5710 A and 2950-3850 A, respectively. The ex-perimental spectrum is reproduced in Fig. 6. The linesat 4190 A and 5115 A correspond to Lyman ghosts oforder 0.55 and 0.45; the line at 3850 A is apparently

__ another grating ghost. The gradual cutoff of the bandbelow 3850 Awis attributed to the incandescent source,weak in uv.

Equations (7a) and (7b) can also be used to explain theresults obtained by Penchina 2 in his scattering experi-ments. Using a monochromatic source at 5461 A,Penchina scanned a single instrument through thevisible region and recorded the settings for which thegreen line was passed as stray light. Setting X =

'3,I X. 5461 A and solving Eq. (7a) for o yields a band from3000 A 2080-2320 A, while Eq. (7b) predicts o in the range

,ded area) a a 3100-3360 A. Both these ranges adhere closely to ther light resulting published results of Penchina.rs is represented. Other values of n and m [Eqs. (5) and (6) ] explain

other scattering bands, but all will be at wavelengthsless than 0. This is because the order of the firstdiffraction must be greater than the order of the seconddiffraction: n > n and 11 = 0, therefore n = 2. In

- 780 X(7 the next simplest case, n = 2 and n = 1. Equations0 - 780 A& (7b) (5) and (6) eliminate to determine a line in the y-O

50 A. plane. From here, the same algebra that led to Eqs.50 inAF. 4, in (7a) and (7b) yields the corresponding Eqs. (8a) and

in Fig. 4,in (Sb). Forn = 2,m = 1, path A:is plotted as a

plttdas0.884Xo - 210 A for Xo < 4700 AI0.667x, + 260 A < < 0..53,,Xo + 1410 A for X > 4700 A;

To test these predictions, an incandescent lamp wasmounted before the entrance slit of a Spex model 1700used as a monochromator with a Bausch & Lomb 600-lines/mm grating, 102 mm square, blazed at 5000 A.Slits were opened to 2 mm X 50 mm. The wave-length was adjusted to various settings in the uv, andthe light from the exit slit was focused on the entranceslit of a second 1700 set up as a spectrometer. Thesecond instrument was then scanned to determine thestructure of the light emerging from the first. Sinceno uv was present in the source, the latter comprisedstray visible light only. The total intensity of lightreaching the second instrument was sufficiently lowthat no scattering effects of the second instrument couldhave influenced the results.

With N = 1800 A, Eq. (7a) predicts doubly dif-fracted light in the range 4410-5130 A. Figure 5 showsthe actual response. The peak at 4000 A is a 0.45 orderLyman ghost line, broadened by slit width. The peakfound at 3850 A is probably a triple diffraction effect,from light reflected twice by the collimating mirrorbetween diffractions in the first and zeroth orders.The intensity is high because the light is relatively wellfocused at the exit slit, as opposed to doubly diffractedlight that is nearly collhiated. Similar peaks werefound, always centered at 3850 A, for 1300 A < o <1900 A. Because of the large number of limiting equa-

path A passes stray light for 2170 A < 0 < 8710 A.

I-.t:

I

4000A 4500 A 5000 A

Fig. 5. Spectrum of stray light for monochromator setting1800 A.

1434 APPLIED OPTICS / Vol. 7, No. 8 / August 1968

§ |

. . . . . . . . . . .

3500A 4000A 5000A

Fig. 6. Spectrum of stray light for2300 A.

5500A

monoehromator

For n = 2, m = 1, path B:

for Xo < 7010 A: 0.535Xo + 170 A

for X0 > 7010 X: 0884X 0 - 2340 AX

Equation (8b) predicts scattering for 2920 < X A.

Both sources of scattering may prove troubwhen the instrument is used in the visible and sregions. These bands have been observed

mentally, but other stray light peaks for X < 0 make- them less conspicuous than the zeroth order scattering,- with > .

Other bands may be predicted with the aid of thegraph (Fig. 3). Appropriate values of n and m aresubstituted in Eqs. (5) and (6), the two are solved

- simultaneously for a given 0, and the result plotted.Since all equations are linear, the results may be

-I generalized for any grating ruling with a simple scale- factor in the constant term of the final equation.

Once the doubly diffracted light has been identified,steps may be taken to eliminate it. One expensive buteffective method is to use more finely ruled gratings

sttig when working in the uv. If X is sufficiently far fromsetting N0, it may be convenient simply to filter out the stray

light.' Penchina has suggested2 masking a narrowhorizontal band in the center of the grating wherea once-diffracted spectrum is returned in focus by

260 A. either concave mirror. This method has been found(8b) consistently effective in eliminating doubly and triply(Sb) diffracted light in all orders, while reducing the efficiency

C 9590 of the instrument by about 30%o.

lesomehort irexperi-

References1. A. Watanabe and G. C. Tabisz, Appl. Opt. 6, 1132 (1967).2. C. M. Penchina, Appl. Opt. 6,1029 (1967).

Meeting ReportsInformation about future meetings should be sent to

P. R. WAKELING, Editorial Consultant WINC, 1500Massachusetts Avenue, N. W., Washington, D. C. 20005

4th Conference on Molecular Spectroscopy,Brighton, 17-19 April 1968

The band was led by Harold Thompson, knightFrom Oxford; he that once plain Thommy hight.Ere that our Sov'reign Liege and Gracious QueenEnnobl6d him, lief lord of light unseen.He unto Brighton, England, call'd his menAnd women too, Professor Josien,Three hundred else besides, a learn6d crewTo talk of features spectroscopic new,For three full days. The seventeenth the dateIn April nineteen hundred sixty-eight.The Metropole Hotel furnish'd fine soup,Mind's food, the Hydrocarbon Research Group,Th' Institute of Petroleum did provide,While sun and rain God chang'd with ev'ry tide.Our first discourse on th' infrared extreme,The ruddy Miller did expound the theme,The height of barriers, the shapes of rings,Of lattice modes and many such like things.Doctor Adams spoke of metal ligandsTheir fields of force and their vibrating bands.Wilkinson "molecular moti6ns"Made all keen for their tea-time poti6ns.We heard how using computers MilwardTransform'd interferograms. Next SheppardSpoke of surface adsorbed molecules.To the technique for sages and for foolsBy Doctor Fahrenfort call'd ATR.

Then ta(i)l(e)s of cock were plenty at ye Bar.Next morn, when the said cock had woken all,The throng returned to the room of ball.Whiffen spoke of ENDOR, resonance doubleSign mysteries made plain to them that trouble.Th' orbit de l'electron celebataireIn nitroxide radicals was made clearBy Monsieur Rassat. Then to gasesWhose fine resonance is not for assesTo bray, but for Professor Carrington.Came we to rapid esr whereonMcLauchlan related. A sudden switchTo Doctor Shields who did the crowd enrichAnd started discussion amongst us all,On spectra stor'd and their retri6val.This vasty problem, wise men did agreeMust solved be ere nineteen eighty three.Photoelectrons and their measurementBy Turner and Bill Price kept all intent.Stoicheff talk'd on Brillouin scatteringEven dolts could follow a smattering.Ellis Lippincott, on laser RamanSpectra showed how even a lemanMight be excited and scatter her rays,Thus must Raman be measur'd in these days,So agreed Hendra: Prof. Delhaye reckon'dTo see spectra in one millisecond.The midnight moon then sent us all to bedAnd rise refresh'd. When the en-NobeledGeorge Porter told how he and all his palsStudied aromatic free radicals.Bennett told of the fast spinning DewarSpecies caught, and scrap'd off with a skewer.Hallam of compounds in a matrix trapp'd,Which Friday morning suitably encapp'd.Then after lunch on this the final dayAll speakers said of nmr their say.First high resolv6d, who but Freeman, Ray,

August 1968 / Vol. 7, No. 8 / APPLIED OPTICS 1435

. . . . .l A ^ ^ l ^ ^ |

Point 0 five Hertz in a most subtil way.While nature is mean with carbon thirteenThis prov'd no handicap to Doctor Leane.Nor yet Rex Richards did she greatly taxHis pulses catch her spills ere they relax.Stejskal pulses to polymers appliesTo seek out their moti6ns as time flies.While Geoffrey Allen sees how they are bredBy using their soluti6ns instead.Lastly Sir Ii-arold yet once more upstoodAnd thanked all, helpers and speakers good.And so he hop'd that it would not be long,Ete once again he weleomed our throng.

11th International Solid-State CircuPhiladelphia, 14-16 February 1968

its Conference,

Reported by K. Preston, Jr., Perkin-Elmer Corporation

The eleventh annual International Solid State Circuits Con-ference (ISSCC), held in Philadelphia last February, continuesto be one of the most significant annual meetings in the solidstate area. As expected, there was heavy emphasis on advancesin integrated circuitry (IC) but also there were some papers ofinterest in optics-related areas.

This year, for the first time, the conference was sponsored bythe five IEEE Professional and Technical Groups that make upthe Solid-State Council: Circuit Theory, Computer, ElectronDevices, Microwave, and Magnetics. The program was signifi-cantly expanded over previous years with approximately 150authors from the U.S.A., Europe, and Asia presenting papers toan estimated gathering of well over a thousand. Fifteen formaldaytime sessions were held on the campus of the University ofPennsylvania with twelve informal evening discussion sessions atthe Sheraton Hotel.

This reporter covered two evening discussion sessions con-cerning areas of interest to the readers of APPLIED OPTICS,namely, memory technology (including optical memories) andimaging mosaic sensors and displays, as well as the formal sessionon new devices and techniques, which included two papers in theelectrooptic area. At the latter session, L. E. Somers GESyracuse presented a paper on electronically switchable displaypanels using a bitter solution grating technique similar to thatreported by H. W. Fuller and R. J. Spain in Optical and Electro-Optical Information Processing (MIT Press, 1965). The basicstructure of the display panel consists of an x,y matrix of columnand row conductors that are used to selectively create stripedomains in a 3 -ju thick nickel iron film. In contact with the filmis a colloidal suspension of magnetic particles (bitter solution)protected by a 100-a thick cover glass. The stripe domain at anyresolution element in the film may be oriented by the x,y excita-tion at that point. This orients the bitter solution particles in agratinglike structure. The panel is illuminated at an angle ofincidence that places the viewing angle at the first order ofdiffracted light from each resolution element. With a 900rotation of the domain structure, the light reaching the viewerfrom the associated resolution element can be varied by 30 to 1.Somers demonstrated a multicolor display from a panel 15.25cm square with fifty elements to 2.54 cm. Microsecond switchingtimes of the magnetic film were reported with a 10-msec responsetime for the colloid. Advantages claimed for this display arethat it is electronically controlled, is nonvolatile owing to thesquare hysteresis loop of the magnetic material, and that bright-ness is governed not by the panel itself (which acts primarily as aswitch), but by the brightness of the illuminating source.

At the same session, K. Preston, Jr. Perkin-Elmer Corporationpresented a paper on an array optical spatial phase modulator.

The phase modulator discussed is a new device called the mem-brane light modulator of MLM. This device is an opticallyflat mirror in its quiescent state. The surface of the mirror isa metallized polymer membrane 1000 A thick supported on acompartmented substructure containing activating electrodes.Surface elements of the mirror can be deflected electrostaticallyon a microscopic scale in order to phase modulate incident re-flected light. An MLI having thirty-eight columns of seventy-four modulating elements in an area of 4 mm by 4 mm wasdescribed. This array requires approximately 50 V to produce a3600 phase reversal of the incident light over a surface element38 A in diameter. Response time is approximately 500 nsec, andat present, no degradation with time has been observed (MLM'shave been cycled several billion times without an observablechange in their characteristics). An optical analog computerwas described using the array MLM as a multichannel inputdevice for use in taking Fourier transforms of thirty-eightelement phase functions. Performance was described as beingdiffraction limited with signal degradations at worst of 6 dBfrom theoretical.

In the evening discussion session on memory technology,G. M. Amdahl IBM Menlo Park took the viewpoint that read-only memories were of little or no interest for digital computation.He pointed out that in reality there are hardly any "fixed data"stored in a typical computer system. For example, supposedlyfixed programs are in actuality constantly being modified atleast to some degree. This means that, in Amdahl's opinion,optical memory must be alterable to be successful. Amdahl alsomentioned requirements for a hierachy of memories where thefaster memories act as "windows" on the slower memories. Hefelt that the typical future computer would require approxi-mately 10' words of 5-psec memory, 10' words of 0.5-jusec "mainmemory," and approximately 103 words of 0.05-psec or "pagingmemory."

F. M. Smits BTL discussed their holographic memory ad-dressed by a 100 X 100 acoustic laser beam deflector which acces-ses an array of 1-mm diam holograms each containing 104 bits.Whatever hologram is accessed forms an image on a semicon-ductor readout matrix. This leads to a 108 bit memory. Accesstime per block of 104 bits was reported as approximately 1 usec.

The session on imaging mosaic sensors and displays waschaired by T. E. Bray GE Syracuse, and covered a multitude ofimage scanning and display techniques. E. I. Gordon BTLdescribed the present state of the silicon vidicon. The targetof this vidicon is an n type silicon slice approximately 50 ,u thickdiffused with an array of p+ diodes spaced approximately 20 .apart. Response time is determined primarily by diffusionlength and in a typical device is of the order of 1 pusec. Althoughbad diodes are still a problem in production, this apparently willsoon be under control, and the Bell System plan to use thesilicon vidicon in their future picture-phones. Extremely long lifeis expected due to the stability of the silicon storage surface.

B. J. Lechner RCA Princeton described their solid state vidiconconsisting of a 256 by 256 array of cadmium sulfide photodiodesaccessed by two 256 CdS integrated access switches. This solidstate vidicon operates in an ordinary raster fashion with timesequential read out. It requires an illumination of approxi-mately 10 m/m'.

In the display area, many approaches were contrasted. Plasmadisplay was discussed and it was pointed out that its efficiencyis low (0.1 lumen output per watt vs approximately 200 lumensper watt for a CRT). Bray described GE's photoconductiveelectroluminescent display which could convert infrared to visibleimages. R. H. Dyck Fairchild, Palo Alto discussed arrays ofphotodiodes and phototransistors using MOSFET technologywhich could operate at levels of 0.1 m/m'. J. Hackney BTL

continued on page 1441

1436 APPLIED OPTICS / Vol. 7, No. 8 / August 1968