Arthur Davis

Masters Paper

University of Rochester, Institute of Optics

Professor Brown

STRAY LIGHT IN CZERNY-TURNER MONOCHROMATORS

A brief history of diffraction gratings and grating mounts in monochromators is offered. The

distinctions of each type of mount along with inherent advantages and disadvantages are

discussed. The "W" configuration Czerny-Turner monochromator is singled out and its

geometry, optical properties, aberrations and sources of stray light are discussed in some

depth. To examine the effects of double diffraction in the layout, a specific system is entered

into high performance optical analysis software. Results from the simulation are shown to

correlate with published results of other authors.

Introduction

In 1785 David Rittenhouse invented the first diffraction grating when he wound some thin

wires along two very fine pitch screws.1 Rittenhouse did not pursue his invention any further.

In 1821 Joseph von Fraunhofer independently repeated Rittenhouse’s experiments and

additionally produced reflection gratings by ruling grooves with a diamond point on a mirror

surface. Fraunhofer was the first to realize the usefulness of diffraction gratings. He used his

gratings for measuring the wavelength of light. He recognized the phenomenon of multiply

diffracted orders and he derived and verified the grating equation.2

M. Czerny and his graduate student A.F. Turner invented one of the most useful methods for

using plano diffraction gratings for spectroscopy in 1930.3 The Czerny-Turner mounting has

remained popular to the present day. Other very popular plano grating mountings were also

invented. To name the most common: Ebert-Fastie mounting4,5,6, Monk-Gillieson mounting7,8,

and Littrow mounting9.

Additionally in 1882 H.A. Rowland described his design and manufacture of the first concave

gratings.10 This eliminated the need for multiple concave mirrors in spectroscopic instruments.

This was an important concept and development for work in the deep UV where every surface

reflection suffers from extremely poor efficiency. His mounting, known as the Rowland circle,

allowed for spectroscopic instruments with only one reflection/diffraction, thereby separating

light into its constituent wavelengths with the absolute minimum loss in energy.

Since Rowland, numerous mountings have been developed for the concave grating. To name a

few: Seya-Namioka mount11,12, Eagle mount13, Abney mount, Paschen-Runge mount and

Wadsworth mount14. Though each mounting has its specific advantages and disadvantages, the

price of concave diffraction gratings is still significantly more than plano gratings. This makes

the Czerny-Turner mounting with its low cost plano-grating and commonplace spherical

mirrors very favorable in modern day instrument design.

In this paper, the most common forms of plane grating mounts will be briefly examined for

optical performance. Then the optical properties of a “W” configuration Czerny-Turner

monochromator will be discussed and sources of stray light will be examined (most notably

1

double diffraction and surface scattering). There are several papers that cover various aspects

of stray light performance in Czerny-Turner monochromators.37,42,43,44,45,46,47,48,49 The results in

these papers are discussed here. In particular, the model presented by Mitteldorf and Landon45

is entered into software packages15,16 and evaluated.

Grating Mounts

In the Littrow mounting9 a single lens is placed in front of the dispersing element as an

autocollimator which both collimates the light before dispersion and focuses it afterwards to

the exit slit. The original Littrow configuration was designed to work with prisms in which

light would be reflected by a mirror or a metallized surface on the last prism. It was first

suggested to replace the prisms with a diffraction grating in the 1880’s.4,17,18 The system

performance is limited by the transmission properties of the lens and to narrow spectral

regions in which the lens performance is approximately achromatic. A schematic of the

Littrow mounting is shown in Figure 1.

Figure 1: Littrow Mounting

The Monk-Gillieson mounting7,8 borrows from the idea of the concave grating Wadsworth

mount as describred in Reference 14. The Wadsworth mount achieves stigmatic imaging by

departing from the Rowland circle in such a way that diffraction occurs normal to the grating.1

In the Wadsworth mount, the concave grating is illuminated with collimated light, in the

Monk-Gillieson mount a plane grating is instead illuminated with convergent light. This

effectively minimizes the number of elements for a plane grating mounting. A disadvantage

however is that there is one optimal focus at only one wavelength thereby requiring the system

to be designed at a high f/#. Also, the bandwidth performance of an instrument using the

2

Monk-Gillieson is limited and typically will not be better than 20 nm.1 A schematic of the

Monk-Gillieson mounting is shown in Figure 2.

Figure 2: Monk-Gillieson Mounting

The most popular mounting for plane diffraction gratings and the main concentration of this

paper is the Czerny-Turner mounting.3 A Czerny-Turner mounting uses two identical off-axis

concave spherical mirrors as the collimating and focusing (camera) elements. The mirrors are

arranged such that coma is cancelled. A significant advantage of this system is that high

performance can be achieved by implementing low cost simple elements: two spherical mirrors

and a plane grating. A typical Czerny-Turner mountings is shown in Figure 3. This is the most

common configuration also known as the “W” configuration as the path of the light would

suggest.

Figure 3: “W” configuration Czerny-Turner Mounting

To alleviate stray light, there is also a crossed beam version of the Czerny-Turner mounting, or

“X” configuration as shown in Figure 4. Although the stray light can be reduced in this type of

mounting, astigmatism is notably worse and the exit image is additionally rotated.19

3

Figure 4: “X” configuration Czerny-Turner Mounting

A third type of configuration possible with the Czerny-Turner mounting is the “U”

configuration. Both the “W” and the “X” configuration mountings can be classified as a subset

of the “Z” configuration.20 The “Z” configuration has the entrance and exit slits on opposing

sides of the diffraction grating. The “Z” shape is the shape that is traced out when the system

is unfolded as in Figure 5. In the “U” arrangement, the exit and entrance slits are on the same

side of the grating as in Figure 6. If the system is again unfolded, the “U” shape is evident.

These distinctive mount variations are pointed out originally by Czerny and Turner.3 Chupp

and Grantz additionally show that spherical mirrors perform much better in “Z”

configurations and parabolic mirrors perform much better in “U” configurations. Also the

aberrations and stray light in a parabolic “U” configuration is superior to an equivocal “Z”

configuration design.20 Although this implies that a “U” configuration may be an optimal

design, it is not considered in depth here. The reason being that parabolas are expensive and

difficult to use in alignment. A “U” configuration monochromator will also require at least one

additional plane mirror for redirecting light to make the system manufacturable.20 Instead, the

much cheaper and easily manufactured “Z” configuration is studied.

4

Figure 5: “W” configuration is a subset of “Z” configuration

Figure 6: “U” configuration Czerny-Turner Mounting

The final monochromator mount that will be mentioned here is the Ebert-Fastie mount. A

diagram of the mount is shown in Figure 7 and can be considered a simplification of the

Czerny-Turner system in which the collimation and focusing mirrors have coincident centers

of curvature.5 The mount was first described by Hermann Ebert in 1889.4 The key feature of

the mount is that one large mirror is used for both collimation and focusing. The usefulness of

this design was undermined in H.H. Kayser’s publication of Handbuch der Spectroscopie in 1900.

Kayser described the mounting as unfeasible because stray light could be directly imaged from

the entrance slit and that such a large mirror was impractical. In fact, the stray light problem is

easily remedied with baffling and the large mirror brings the advantage of making one single

adjustment to replace the two adjustments of the two separate mirrors in a Czerny-Turner

design.6,21

In 1948, William G. Fastie reinvented the mounting while working on a project to develop a

spectroscopic system for industrial steel analysis.21 Fastie realized the coma contributions of

5

each mirror reflection was subtractive, while the astigmatism was additive. To get good

throughput then, curved entrance and exit slits were indicated to match the aberrated spectral

image. It was the singular mono mirror of the Ebert mount which prompted Fastie to center

the slit radius of curvature about the central axis of the mirror. This lead him to the important

discovery that when the slit curvature is centered about the central axis of the monochromator

(for the Ebert mount and for Czerny-Turner mountings in general) the wavelength error of the

transmitted spectra is zero no matter what the wavelength.6,21

Figure 7: Ebert-Fastie Mounting

The Grating Equation

The well known grating equation is described in many optical texts.22,23,24,25 It is given in

Equation 1 :

)sin(sin βαλ += dm ( 1 )

where λ is the wavelength, d is the groove spacing or distance between adjacent rulings, α is

the angle of incidence (defined as positive), β is the angle of diffraction (defined as positive if it

is on the same side of the grating normal as α and negative otherwise) and m is the integer

diffracted order (orders are negative if they are diffracted on the negative side of zero order

and positive otherwise).

Equation 1 takes on a different form when considered in a constant deviation

monochromator. The Czerny-Turner monochromator is a constant deviation monochromator

in which the wavelength is tuned by rotating the grating. Two new variables can then be

6

defined: the deviation angle 2K and the scan angle φ. Their definition is given in Equation 2

and Equation 3. The resulting change of variables to Equation 1 is given in Equation 4.25 A

summary of the geometry variables is depicted in Figure 8.

constant)( 2 βα −=K ( 2 )

) of (function 2 λβαφ += ( 3 )

φλ sincos2 Kdm = ( 4 )

θ1

θ2

φ

K2K

β

α

ExitSlit

EntranceSlit

Grating

Mirror 1

Mirror 2

Figure 8: Definition of grating/monochromator geometry variables.

Because of the nonlinear dependence of wavelength on scan angle, special attention must be

taken to rotate the grating with what is called a sine bar mechanism.25 The angle of the grating

is proportional to the arcsine of the desired wavelength. Because of this relation, for a constant

slit width, the bandpass of the instrument is variable. To compute the bandpass of the

instrument, Equation 4 is differentiated on wavelength with respect to the grating diffraction

angle. By scaling to the focal length of the system, f, the reciprocal linear dispersion or plate

factor, P, is found as given in Equation 5:25

7

( )mf

KdP −=

φcos ( 5 )

For a given constant spectral bandwidth, ∆λ, the needed slit width is given by Equation 6:26

)cos( Kdmfx

−∆

=∆φλ

( 6 )

A plot of this function for m=1, f=74.8 mm, ∆λ=5nm, 1/d=600 lines per mm, and K=3.37°

(these values will be used in the monochromator design for later analysis) are shown in Figure

9.

0 200 400 600 800 1000 1200 14000.22

0.225

0.23

0.235

0.24

0.245

Wavlength (nm)

Slit

Wid

th (m

m)

.245

.22

∆x λ( )

14000 λ

Figure 9: Variable Slit Width for Constant Bandpass vs. Wavelength

If a constantly variable slit width is not available, Rosfjord et al. describe an algorithm for best

matching the slit width with a given set of available finite slits.26 In this paper, a constant slit

width will be assumed. For most industrial and commercial applications, the small variation in

bandpass does not justify the added cost of making a variable slit width. In this example, the

variation of bandpass for a fixed slit width of ∆x=.225 mm, is shown in Figure 10. It is often

8

sufficient to design for the specified resolution (in this case ~5 nm) at the worst performance

wavelength. All other wavelengths will then have a bandpass equivalent or better.

0 200 400 600 800 1000 1200 14004.6

4.7

4.8

4.9

5

5.1

Wavlength (nm)

Ban

dwid

th (n

m)

5.1

4.6

∆λ λ( )

14000 λ

Figure 10: Variable Bandpass for Constant Slit Width vs. Wavelength

Aberrations

The image of the entrance slit on the exit slit in a monochromator contains many different

types of aberrations. Using the terms coma, spherical and astigmatism are not accurate by their

usual third order definitions. Instead the following redefinition of these terms as described by

Shafer et al.27 is adopted:

(1) Coma is an asymmetry of the image of the entrance slit and is orthogonal to the curved

exit slit. This will produce an asymmetry of the spread function of the spectrometer and

hence an asymmetry in the contour of the observed line.

(2) Astigmatism is an extension of the image of a point of the entrance slit. The extended

point image, if properly curved slits are used, is tangential to the curve of the exit slit.

9

(3) Spherical aberration is a symmetrical spreading of the image of a point of the entrance

slit. Spherical aberration will produce a symmetrical broadening of the spread function

and hence a widening of the line contour with a possible reduction in resolution or

contrast.

Coma

Shafer et al.27 derive the condition for zero coma in a Czerny-Turner monochromator given

below in Equation 7:

233

133

1

221

22

coscoscoscos

sinsin

θαθβ

θθ

⋅= R

R ( 7 )

where R1 and R2 are the radii of curvature of the first and second monochromator mirrors

respectively and θ1 and θ2 are the incident and reflected angles to the first and second

monochromator mirrors respectively. The variables are defined graphically in Figure 8.

In a symmetrical type Czerny-Turner arrangement, R1=R2 and θ1=θ2. Under these conditions

Equation 7 simplifies to Equation 8:

βα = ( 8 )

which indicates that for absolute coma correction, referring to Equation 2 and Equation 3, it is

required to have either a zero constant deviation angle (K=0) or a zero scan angle (φ=0). A

zero scan angle is exactly the zero order imaging condition in a symmetric Czerny-Turner

Mounting. In zero order, the grating acts as a mirror, imaging all the light that is not dispersed

into the multiple orders as undiffracted white light. This is not useful for spectral analysis. The

remaining condition then is to set a zero scan angle. This is the Littrow condition of the

grating, in which the diffracted light propagates back upon the incident beam. The Littrow

configuration obviously will not work for a Czerny-Turner mount. In practice, a small amount

of coma is acceptable and can be minimized by keeping the scan angle, K, as small as possible.

10

This notion of keeping the scan angle small is contrary to the Cary principle for rejecting

multiply diffracted stray light as will be discussed later.

Shafer et al.27 offer solutions for further minimizing coma by allowing R1≠R2 and θ1≠θ2. Such

an arrangement is necessarily asymmetrical. Additionally in the asymmetric case for θ2>θ1

astigmatism is always greater.27

Astigmatism

Astigmatism as considered in monochromators manifests only a pure distortion of the image.

Its effect can consequently be minimized by appropriately curving the slits. Fastie discovered

that astigmatism could be compensated for if he curved the slits about the central axis of his

Ebert monochromator.6,21 Shafer et al.27 generalize the slit curvature for asymmetrical Czerny-

Turner mountings. Accordingly, they find that slit curvature is a function of the distance from

the entrance slit to the collimating mirror; the position of the focusing mirror has no effect.

They also find that the curvature approximates an ellipse and degenerates to a circle only for

the Fastie condition for which the center of curvature of the collimating mirror lies on the

central axis. Additionally if R1≠R2, the radius of the exit slit is (R2/R1)×(radius of the entrance

slit).6,27

Several authors suggest that astigmatism can be minimized by physically warping the

grating28,29, by using toroidal mirrors30 and by using lenses31. Each has varying inherent

advantages and disadvantages that are beyond the scope of this paper.

In this investigation, straight slits will be considered instead of curved slits. Several authors6,32

derive the wavelength error from using straight slits as given in the following Equation 9:

2

2

8 fLλ

δλ = ( 9 )

where L is the slit length. A graph of Equation 9 for several slit lengths is shown in Figure 11

for the previously defined focal length of f=74.8 mm.

11

0 200 400 600 800 1000 1200 14000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

L=1 mmL=2 mmL=3 mmL=4 mmL=5 mm

Wavelength (nm)

Wav

elen

gth

Erro

r (nm

)

.8

0

δλ1 λ( )

δλ2 λ( )

δλ3 λ( )

δλ4 λ( )

δλ5 λ( )

14000 λ

Figure 11: Wavelength Error for Straight Slits vs. Wavelength

For an arbitrary choice of slit height L=3mm, we see that the wavelength error will not be

greater than 0.3 nm.

Spherical Aberration

In a symmetric Czerny-Turner monochromator, there is not a lot that can be done to reduce

spherical aberration. Although relatively small compared to the coma component, it is inherent

in the Z-configuration layout and is additive at each mirror.3,20 One solution is to use parabolic

mirrors which have no spherical aberration. Shafer and London33 point out that in the Z-

configuration, however, coma is additive when parabolic mirrors are used. Chupp and Grantz20

show that if parabolic mirrors are instead used in the U-configuration that coma is subtractive.

Chupp and Grantz20 additionally show by raytracing that a U-configuration parabolic mirror

monochromator has the minimum point spread function of all comparable monochromator

mounts. The design and properties of this type of system are first examined in the literature by

Hill34 and Chupp and Grantz20. Examples of this configuration are given in Figure 1220. Gil

and Simon35,36 study the aberration properties of this mount further in Reference 35 and do a

comparison of the aberration properties with various mount configurations in Reference 36.

12

Figure 12: U-configuration Mounting for minimizing coma, astigmatism and spherical aberration. The concave mirrors are parabolic. Reproduced from Reference 20.

Stray Light

A significant problem in monochromator performance is the issue of stray light. When

measuring low signals, stray light is evident as a response at an unwanted wavelength causing a

measurement error. The distinction between stray light and scattered light as called out by

Geikas37 is adopted here:

“Stray Light” shall refer to all noise which is detectable at the exit aperture.

“Scattered Light” is that which is a result of surface scattering from a grating.

Multiple Orders

Assuming no other sources of stray light in a monochromator mounting, the grating itself will

be a source of stray light due to multiple order diffraction. This can be illustrated by rewriting

Equation 4 into Equation 10 as follows:

13

=

Kdmcos2

arcsin λφ ( 10 )

Typically, the grating is used in the first order: m0=1. We can see then for a given wavelength:

λ0, a solution for a given scan angle is satisfied whenever the product of another diffracted

order: m1 with another wavelength λ1 is equal to the product of m0 with λ0 as given in

Equation 11:

1100 λλ mm = ( 11 )

For m0=1, multiple order stray light will only occur for higher orders and consequently from

lower wavelengths. Multiple order diffraction is, of course, not a problem if there is no signal

from the source to cause the generation of a diffracted order or if the detector is not sensitive

to the lower wavelength. For example, at 400 nm with a tungsten source, no special attention

need be made to prevent second order 200 nm light from reaching the detector. A tungsten

source will emit negligible amounts of 200 nm light into the monochromator. However, to

extend the example, second order diffraction will be a problem at 800 nm where the tungsten

source emits a substantial amount of 400 nm energy that will be partially directed into the

second order and co-propagate with the 800 nm first order spectra. To alleviate this problem a

judicious choice of order sorting filters is required. The number of filters and their type will

depend upon the stray light requirements of the instrument and the type(s) of source(s) used.

If multiply diffracted light is the only source of stray light, the application of high pass filters

are indicated. An example of good filters to use from the Schott catalog38 are shown in Figure

13. In our example, we may choose an OG-590 filter at 800 nm which will reject our

problematic 400 nm second order (and all higher order diffraction) stray light.

14

Figure 13: Some typical High Pass filters for Multiple Order Stray Light Rejection available from Schott Glass Technologies.38

Spectral Impurity

Any stray light that is not accounted for by Fraunhofer diffraction may be regarded as

“spectral impurity” as summarized in Figure 14.39 The first three types (a), (b) and (c), are due

to Fraunhofer or edge diffraction and as such do not fit the definition for spectral impurity

although they are a source of stray light. To minimize this effect, as in case (c), it is

recommended to underfill the grating with Gaussian illumination. In practice this is rarely a

detectable problem.40,57 The (d) type are from ghosts and are only present in ruled gratings.

There are two types of ghosts: Rowland ghosts and Lyman ghosts. Rowland ghosts appear as

spikes close to the diffracted order and are due to long-term periodic errors in the groove

spacing.39,40 Modern day ruling engines with interferometric feedback control have nearly

eliminated Rowland ghosts.40 Lyman ghosts appear as spikes widely separated from the

diffracted order and are due to short-term periodic errors in the groove spacing.39,40 Lyman

ghosts are still unsuppressed by modern day ruling engines.40 Satellites as depicted in (e) are

caused by groove location errors in ruled gratings that cover a significant portion of the grating

but are not periodic. Satellites will cause an asymmetry of the diffracted order.39,40 Grass,

shown in (f), appears in ruled gratings as a faint fuzz between orders and is due to short term

random variations of groove locations.39,40,57 Diffuse scatter, (g), occurs for both holographic

and ruled gratings and is due to surface roughness, random errors which have no preferred

15

direction, dust and scratches.39,40,57 For holographic gratings, an additional source of diffuse

scatter can occur by inadvertent illumination of the interferometer apparatus which will

effectively record itself as a hologram in the grating photoresist.39 On occasion, the diffuse

scatter in a holographic grating will be seen as a halo about the diffracted order. This is due to

“comet marks” which can appear when the photoresist is spun onto the grating blank and dust

is present on the surface.41,57 An additional source of diffuse scatter in a ruled grating can occur

by periodic or random variations in ruling depth.40 Finally, (h) shows stray light due to surface

plasmon scattering which is caused by the interaction of the incident field with the rough

conductive grating surface.39 It is exhibited in all metallic coated gratings and is dependent on

the polarization and the grating material.39

Figure 14: Summary of forms of spectral impurity. Reproduced from Hutley, Reference 37.

Double Diffraction

Welford42 points out that all in-plane systems may suffer from stray light due to part of the

diffracted spectrum falling on the grating. Watanabe and Tabisz43 illustrate possible light paths

16

for double and triple diffraction in an Ebert-Fastie mounting. Several authors44,45 show

separate paths light may take in a Czerny-Turner monochromator for double diffraction as

shown in Figure 15 and Figure 16. This stray light is not caused by scatter or grating artifacts.

It is an inherent part of the in-plane mounting of the Czerny-Turner monochromator.44

Figure 15: Double Diffraction Path 1.44

Figure 16: Double Diffraction Path 2.44

M.V.R.K. Murty46 states the Cary principle of monochromator design which may be used to

avoid multiple diffraction problems as follows:

Arrange the collimator mirror and focusing mirror in such a way that the normals to the

inner edges of these mirrors will not pass through the aperture of the dispersing element.

This condition is illustrated diagrammatically in Figure 17 as taken from Murty46.

17

Center of curvature

Entrance Slit

Grating

Mirror 1

Mirror 2Center of curvature

Exit Slit

Figure 17: Illustration of the Cary Principle. The mirror normals at the edges do not intercept the grating.

Murty goes on to calculate the minimum off axis angles required to avoid double diffraction

and finds that the resulting instruments length is increased by 50-60% from typical small angle

monochromators.46 By increasing the off axis angles to avoid double diffraction, the resolution

of the instrument is compromised due to increased aberrations, particularly coma and

astigmatism.33,46,47 Murty suggests that it is perhaps simplest to use small off-axis angles for

good imaging and a central strip mask across the grating.46 Hawes argues that the increase in

off axis angle for medium sized instruments rarely increases the aberrations sufficiently to limit

resolution as evidenced by a number of Cary spectrophotometer models that he cites.47

Several authors suggest using a central strip mask across the grating.44,48 Because the double

diffraction occurring at the grating is an image of either slit, the mask need only occlude a

small central region of the grating so as to absorb all of the spurious spectra. An illustration of

how to mask the grating is given in Figure 1844.

18

E x i t S l i t E n t r a n c e

S l i t M a s k

G r a t i n g

Figure 18: Face on view of a masked grating to prevent double diffraction.44

An undesirable consequence of using the grating mask is a reduction in the signal. 20,43,44,49 To

minimize this energy loss, Pribram and Penchina determine the minimum size of the mask for

stray light reduction.49

Several authors also suggests designing the instrument out of plane. That is, the entrance slit

and exit slit are symmetrically above and below the grating. In this way, the diffracted spectra

can be designed to miss the grating completely, avoiding multiple diffraction and energy loss.

The trade off for using this technique is that aberrations are made worse.20,42,44,49,50,51 If the

application justifies the cost, multiply diffracted light can be reduced by the tandem operation

of two monochromators.43

Software Analysis

Mitteldorf and Landon45 do a theoretical and experimental investigation of doubly diffracted

light for the in-plane Czerny-Turner design of a Spex model 1700 with a Bausch and Lomb

600 lines/mm grating blazed at 500 nm. The Richardson Grating Laboratory, formerly of

Bausch and Lomb, still has this grating available in its catalog (number: 35-53-260) with a

corresponding efficiency curve. This, in conjunction with the information provided by

Mitteldorf and Landon, is sufficient information to set up the system in software15,16 for

analysis.

The specifications are first entered into OSLO Optical Design Software15. The following is a

printout from OSLO showing the system parameters:

19

*LENS DATA Spex model 1700 SRF RADIUS THICKNESS APERTURE RADIUS GLASS SPE NOTE OBJ -- 50.000000 1.500000 AIR AST -- -- 2.500000 A AIR * 2 -1.4960e+03 -- 51.000000 REFL_HATCH * 3 -- -- 51.000000 REFL_HATCH * Grating 4 -1.4960e+03 P -- 51.000000 REFL_HATCH * 5 -- -- 10.000000 AIR * Dummy 6 -- -- 10.000000 AIR 7 -- -- 10.000000 AIR IMS -- -- 10.000000 *TILT/DECENTER DATA 2 DT 1 DCX -- DCY -- DCZ 698.000000 GC 1 TLA -3.368990 TLB -- TLC -- 3 DT 1 DCX -- DCY 75.000000 DCZ 63.000000 GC 1 TLA -- TLB -- TLC -- 4 DT 1 DCX -- DCY 150.000000 DCZ 698.000000 GC 1 TLA 3.368990 TLB -- TLC -- 5 DT 1 DCX -- DCY 150.000000 DCZ -50.000000 GC 1 TLA -- TLB -- TLC -- *WAVELENGTHS CURRENT WV1/WW1 WV2/WW2 WV3/WW3 1 0.550000 0.200000 1.100000 1.000000 1.000000 1.000000 *OPERATING CONDITIONS: SYSTEM NOTES 1: Bausch and Lomb 600 lines/mm grating 102 mm square blazed at 500 nm 2: Slits: 2mm x 50 mm

An example raytrace is shown in Figure 19. The plotted wavelengths are: 400 nm (blue), 500

nm (green) and 600 nm (red). The grating is set to image 500 nm through the exit slit. It is

apparent that the 600 nm rays will be incident upon the grating when the grating is tuned for

500 nm. Also note, in Figure 19, that although 600 nm rays clearly intercept the grating, they

continue undeviated. This is because OSLO is a sequential raytracing design package. A

sequential raytrace will only intercept (and must only intercept) the rays with the geometry

defined immediately after the current definition in the lens stack. In this instance, the exit slit

comes after the monochromator mirror and so the grating is ignored. For stray light analysis

then, a non-sequential raytracing package is required.

20

Figure 19: An example raytrace of the Spex model 1700 with the grating tuned for 500 nm.

ASAP Optical Analysis Software16 is a non-sequential raytracing package capable of analyzing

stray light. To enter the system geometry into ASAP, the lens file specifications of OSLO were

imported into ASAP and adjusted where necessary. ASAP is a Fortran based analysis package.

The code that was written for this paper to perform the appropriate analysis is given in

Appendix 1.

An example of the data output from running the stray light analysis program is shown in

Appendix 2. This format is not particularly informative. The data can be extracted and

converted into a more useful format that can be plotted in a spreadsheet by the application of

some PERL52 code that was written for this paper and is given in Appendix 2 named

arrvals3.pl. An example of the resulting output is also given in Appendix 2.

In the interest of raytracing expediency, the efficiency profile of the grating was not included in

ASAP during the actual raytrace. Instead, the mathematically identical process of multiplying

the resulting flux values with the grating efficiency is much quicker and used instead. The

grating efficiency curve as reproduced from Reference 53 is shown in Figure 20.

21

Figure 20: Grating Efficiency as reproduced from Reference 53.

To make use of the information, the graph is digitized with Tracer54. The resulting data are in

small non-integer increments. In order to combine the s and p polarization data the two curves

need to be averaged with each other. To accomplish this, the data points need to be forced to

overlap. A linear interpolation routine which can resample the data at arbitrary increments is

written in PERL to accomplish this and is given in Appendix 3 named resamp.pl. The

routine is used to resample the grating efficiency data at 1 nm increments.

Because only a finite number of rays can be used for a computer raytrace program, a certain

amount of error is expected in each raytrace. When successive raytraces are done at varying

wavelengths, a plot of the data will consequently look noisy. See Figure 21. To smooth the

data, a boxcar routine is written in PERL which selects data points in 1 nm increments and

averages about its nearest neighbors. The routine is given in Appendix 3 named avgsamp.pl.

The result of applying the routine is plotted in Figure 22. The data is now ready to be

multiplied with the grating efficiency data. The values are entered into a spreadsheet and

multiplied by the squared values of the grating efficiency values. The grating efficiency is

squared to account for the rays intercepting the grating twice.

22

180nm Stray Light

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520

Wavelength (nm)

Effic

ienc

y

Raw Data

Figure 21: Unsmoothed Raytrace Results

180nm Stray Light

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520

Wavelength (nm)

Effic

ienc

y

Averaged

Figure 22: Raytrace Results Smoothed with avgsamp.pl

Before examining the final results, we would like to acquire data from Mitteldorf and Landon45

to make a comparison. The results published in Mitteldorf and Landon45 are given in Figure

23. Again Tracer54 is used to acquire the data, and resamp.pl is used to linearly interpolate the

data in 1 nm increments. The results are plotted with the properly scaled values of the raytrace

results in Figure 24.

23

Figure 23: Measured Stray Light at 180 nm as published in Reference 45.

180nm Stray Light

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520

Wavelength (nm)

Effic

ienc

y

Paper Measured Normalized ASAP Trace

Figure 24: Comparison of Raytrace Data to Reference 45 Data.

From Figure 24 we notice reasonable agreement between the raytrace results and the measured

data from Mitteldorf and Landon45. There will of course be differences because stray light in

an instrumental measurement includes all sources of stray light, whereas the raytrace

performed in ASAP considered only multiple diffraction effects. For instance, Mitteldorf and

24

Landon45 point out that the little peak at 400 nm is caused by a Lyman ghost line broadened by

the slit width.

Mitteldorf and Landon45 expected to see double diffraction as a source of stray light by

geometrical calculation in the wavelength range of 441-513 nm. Both data sets would seem to

agree. However, Mitteldorf and Landon45 did not expect to see a peak at 390 nm and

hypothesize that it was due to triple diffraction. Because ASAP is not limited by any number of

reflections, the artifact shows up in the raytrace as well. As seen in Figure 22 the raytrace peak

at 390 nm was much stronger before we scaled it down by the waning efficiency values of the

grating at that wavelength (see Figure 20). This efficiency value is only appropriate if the

grating is used in first order. Double diffraction need not occur from spectra imaged from the

first order. Higher orders, negative orders or even zero order can be reimaged by the optics

through the exit slit. If this is the case, as is likely, for triple diffraction, applying the efficiency

value of the grating in the first order to the curve is invalid. To get a more accurate raytrace,

the efficiency of the grating in multiple orders would need to be measured, and applied on a

ray by ray basis, appropriately scaled depending on which order the ray is diffracted into by the

grating. This is certainly a plausible task, but is beyond the scope of this paper.

Scattered Light

When holographic gratings are used, the only significant source of stray light is from grating

scatter in a correctly designed system.37,55,56 The surface scatter from the grating is generally an

order of magnitude in excess of that of a mirror.57

When measuring stray light passing through an exit slit, the amount of grass is proportional to

the slit width and the amount of diffuse scatter is proportional to the area of the slit.57

Consequently, any measured values of stray light must include both the angular slit width and

the slit height.57

The scattering from a holographic grating is given by the same expression as for mirrors37 as in

Equation 1237,58,59:

25

( )λσ

λπσ

<<−=

−

24

1 eS ( 12 )

Where S is the fraction of diffusely scattered light and σ is the RMS surface roughness. Geikas

relates this value to the Bidirectional Reflectance Distribution Function (BRDF)60,61 with the

assumption that the incident field on the grating is monochromatic and is given in Equation

1337:

( )λη

λ∆⋅⋅⋅=

∆ SPLf

Pf

21BRDF ( 13 )

where ∆λ is the monochromator bandwidth, P is the inverse linear dispersion defined in

Equation 5, f is the focal length, η is the diffraction efficiency of the grating for the incident

monochromatic light, L is the slit length and S(∆λ) is the scatter function taken from Geikas37

as shown in Equation 14:

( )

( ) ( )

( )∫

∫

∫ ∫∞

+

−

−∞

+

+

=∆0 2

2

2

02

0

0

0

0

w

w

w

w

dH

dHdH

dSλ

λ

λ

λ

λλ

λλλλ

λλ ( 14 )

where w is the slit width and H(λ) is the spectral irradiance in units of Watts/mm2/nm. S(∆λ)

then has units of inverse nanometers. This indicates that the total integrated stray light

function is equal to the ratio of all extraneous wavelength stray light to the energy in the

analytical bandpass.

Woods et al.55 adopt the grating distribution function (GDF) as a standard for measuring

grating scattered light. The GDF expresses the fractional scatter value per spectral bandpass as

a function of wavelength displacement in the dispersion plane only.55 Woods et al.55 argue that

26

this is valid because the grating scattered light in the plane of diffraction is usually the only

important component for spectrometer operation. This is not entirely true as it has been

pointed out that stray light is closely related to the slit height. Nevertheless, if a holographic

grating is being used, it may be possible to correlate the scattered light in the diffraction plane

with the entirety of the grating scattered light. This would be much more difficult with a ruled

grating because the scattered light in the diffraction plane would only represent a portion of a

total signal containing ghosts, satellites and grass.

Conclusion

In this paper the most common forms of monochromator mountings were briefly examined.

The Czerny-Turner mount was singled out and studied further. The various components that

affect image quality and aberrations were considered. Further, the most important sources of

stray light and how to mitigate these sources were regarded. The issue of double diffraction

was examined in some detail by using raytrace software to compare the theoretical and

measured results published in the spectroscopic literature.

27

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4 Hermann Ebert, “Zwei Formen von Spectrographen”, Annalen Der Physik und Chemie, Vol. 38, pp. 489-493, 1889.

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6 William G. Fastie, “Image Forming Properties of the Ebert Monochromator”, Journal of the Optical Society of America, Vol. 42 No. 9, p. 647-651, Sep. 1952.

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20 V.L. Chupp and P.C. Grantz, “Coma Canceling Monochromator with No Slit Mismatch”, Applied Optics, Vol. 8 No. 5, p. 925-929, May 1969.

21 William G. Fastie, “Ebert Spectrometer Reflections”, Physics Today, p. 37-43, Jan. 1991.

22 See for example pp. 25-28: Reference 1.

23 See for example pp. 424-434: Eugene Hecht with contributions by Alfred Zajac, OPTICS, Second Edition, Addison-Wesley Publishing Company, Massachusetts, May, 1990.

24 See for example pp. 23-26: Reference 2.

25 Christopher Palmer and Erwin Loewen, “Diffraction Grating Handbook”, Second Edition, Spectronic Instruments, 1994.

28

26 Kris M. Rosfjord, Ricardo A. Villalaz and Thomas K. Gaylord, “Constant-bandwidth scanning of the Czerny-Turner

monochromator”, Applied Optics, Vol. 39 No. 4, pp. 568-572, Feb. 1, 2000.

27 Arthur B. Shafer, Lawrence R. Megill, and LeAnn Droppleman: “Optimization of the Czerny-Turner Spectrometer”, Journal of the Optical Society of America, Vol. 54 No. 7, pp. 879-887, July 1964.

28 Murphy L. Dalton Jr., “Astigmatism Compensation in the Czerny-Turner Spectrometer”, Applied Optics, Vol. 5 No. 7, pp. 1121-1123, July 1966.

29 John P. Schwenker, “Astigmatism-corrected gratings for plane grating-spherical mirror spectrographs”, Applied Optics, Vol. 31 No. 28, Oct. 1 1992, pp. 6102-6106.

30 Arthur B. Shafer, “Correcting for Astigmatism in the Czerny-Turner Spectrometer and Spectrograph”, Applied Optics, Vol. 6 No. 1, pp. 159-160, Jan. 1967.

31 William T. Foreman, “Lens Correction of Astigmatism in a Czerny-Turner Spectrograph”, Applied Optics, Vol. 7 No. 6, pp. 1053-1059, Jun. 1968.

32 C.S. Rupert, “Slit Curvature in Grating Monochromators Employing Single or Multiple Diffraction”, Journal of the Optical Society of America, Vol. 42 No. 10, pp. 779-781, Oct. 1952.

33 Arthur B. Shafer and Donald O. Landon, “Comments on Multiple Diffracted Light in the Czerny-Turner Spectrometer”, Applied Optics, Vol. 8 No. 5, pp. 1063-1064, May 1969.

34 R.A. Hill, “A New Plane Grating Monochromator with Off-Axis Paraboloids and Curved Slits”, Applied Optics, Vol. 8 No. 3, pp. 575-581, Mar. 1969.

35 M.A. Gil and J.M. Simon, “New plane grating monochromator with off-axis parabolic mirrors”, Applied Optics, Vol. 22 No. 1, Jan. 1, 1983, pp. 152-158.

36 M.A. Gil and J.M. Simon, “Aberrations in plane grating spectrometers”, Optica Acta, Vol. 30 No. 6, pp. 777-806, 1983.

37 George I. Geikas, “Stray Light From Diffraction Gratings”, SPIE Vol. 675, Stray Radiation V, pp. 140-151, 1986.

38 SCHOTT Glass Technologies Inc., 400 York Avenue, Duryea, PA 18642, USA, Tel. 717-457-7485; FILTER '98 Software, Catalog Optical Glass Filter, Version 1.1US.

39 See p. 51 and pp. 140-146: Reference 2. Reference called to: Lyman, T. (1901). Phys Rev. Vol. 12, p. 1. Wood, R.W. (1924). Phil. Mag. Vol. 48, p. 497. Gale, H.G. (1937). Astrophys. J., Vol. 85, p. 49.

40 See p. 402-409: Reference 1.

41 See p. 107: Reference 2.

42 W.T. Welford, “Stigmatic Ebert-Type Plane Grating Mounting”, Journal of the Optical Society of America, Vol. 53, p. 766, 1963.

43 A. Watanabe and G.C. Tabisz: “Multiply Diffracted Light in Ebert Monochromators”, Applied Optics, Vol. 6 No 6, pp. 1132-1134, Jun. 1967.

44 Claude M. Penchina, “Reduction of Stray Light in In-Plane Grating Spectrometers”, Applied Optics, Vol. 6 No. 6, pp. 1029-1031, Jun. 1967.

45 Joshua J. Mitteldorf and Donald O. Landon “Multiply Diffracted Light in the Czerny-Turner Spectrometer”, Applied Optics, Vol. 7 No. 8, p. 1431-1435, Aug. 1968.

46 M.V.R.K. Murty, “Cary Principle in Monochromator Design”, Applied Optics, Vol. 12 No. 9, pp. 2018-2020, Sep. 1973.

47 Roland C. Hawes, “Multiply Diffracted Light in the Czerny-Turner Spectrometer”, Applied Optics, Vol. 8 No. 5, p. 1063.

48 John E. Tyler and Raymond C. Smith, “Submersible Spectroradiometer”, Journal of the Optical Society of America, Vol. 56, pp. 1390-1396, Oct. 1966.

49 John K. Pribram and Claude M. Penchina, “Stray Light in Czerny-Turner and Ebert Spectrometers”, Applied Optics, Vol. 7 No. 10, pp. 2005-2014, Oct. 1968.

50 R.F. Jarrell, The Encyclopedia of Spectroscopy, G.L. Clark, Ed. (Reinhold Publishing Corp., New York, 1960), p. 180.

51 K.D. Mielenz, J. Res. Natl. Bur. Std., Vol. 68C, 195, 201, 205, 1964.

29

52 PERL for Win32, ActivePerl 522, ActiveState Tool Corp., Copyright 1996-2000. ActivePerl is freely available from:

http://www.ActiveState.com/pw32

53 Richardson Grating Laboratory, Diffraction Gratings

54 Tracer, Version 1.3, Marcus Karolewski, Feb. 2000, Freeware, ftp://pub/simtelnet/win95/science/tracer13.zip.

55 Thomas N. Woods, Raymond T. Wrigley III, Gary J. Rottman and Robert E. Haring, “Scattered-light properties of diffraction gratings”, Applied Optics, Vol. 33 No. 19, pp. 4273-4285, 1 Jul. 1994.

56 M.R. Sharpe and D. Irish, “Stray light in diffraction grating monochromators”, Optica Acta, Vol. 25 No. 9, pp. 861-893, 1978.

57 J.F. Verrill, “The specification and measurement of scattered light from diffraction gratings”, Optica Acta, Vol. 25 No. 7, pp. 531-547, 1978.

58 H.E. Bennett and J.O. Porteus, Journal of the Optical Society of America, Vol. 51, p. 123 (1961).

59 H.E. Bennett, “Specular Reflectance of Aluminized Ground Glass and the Height Distribution of Surface Irregularities”, Journal of the Optical Society of America, Vol. 53 No. 12, pp. 1389-1394, Dec. 1963.

60 Fred E. Nicodemus, “Directional Reflectance and Emissivity of an Opaque Surface”, Applied Optics, Vol. 4 No. 7, pp. 767-773, Jul. 1965.

61 F.E. Nicodemus, “Reflectance Nomenclature and Directional Reflectance and Emissivity”, Applied Optics, Vol. 9 No. 6, pp 1474-1475, Jun. 1970.

30