An experimental investigation of immersed gratings

Mon. Not. R. Astron. Soc. 312, 57±69 (2000)

An experimental investigation of immersed gratings

D. Lee1,2w and J. R. Allington-Smith1

1Department of Physics, University of Durham, South Road, Durham DH1 3LE2Anglo-Australian Observatory, PO Box 296, Epping, NSW 1710, Australia

Accepted 1999 September 6. Received 1999 August 2; in original form 1999 June 2

A B S T R A C T

A generic problem with spectrographs equipped with conventional diffraction gratings is

that the maximum attainable spectral resolution scales inversely with the telescope aperture

for a fixed grating dimension and angular slit width. It has long been realized that immersed

gratings, where a prism is attached to the surface of a reflection grating, offer a means to

bypass this limit. We show how, for the case of the Gemini Multiobject Spectrographs, the

maximum spectral resolution may be approximately doubled, or, equivalently, how the same

spectral resolution may be obtained with a wider slit, resulting in improved throughput when

observing extended objects.

After reviewing the theory of immersed gratings, we present experimental verification of

the theory and experimentally quantify two potential drawbacks: reduced throughput at

blaze, and ghost images. We show that these effects are small and conclude that the benefits

greatly outweigh the disadvantages.

Key words: instrumentation: spectrographs ± techniques: spectroscopic.

1 I N T R O D U C T I O N

The potential of immersed gratings to increase the maximum

attainable spectral resolution of spectrographs equipped with

conventional gratings has been explored by e.g. Dekker (1987)

and Wynne (1989, 1990a,b, 1991, 1992). The spectral resolving

power at wavelength l can be expressed as

R ;l

Dl� mlrW

xDtel

; �1�

where Dl is the width of the spectral resolution element, m is the

spectral order, r is the ruling density, x is the angular width of the

slit projected on the sky, Dtel is the diameter of the telescope

aperture and W is the length of the intersection of the collimated

beam with the plane of the grating. It can be seen that, for constant

W (a constraint imposed by the maximum attainable camera

aperture), and constant ruling density (a constraint imposed by

grating technology), the resolving power is inversely proportional

to the telescope aperture for fixed slit width. For large telescopes,

this implies a reduction in the maximum resolving power unless

the instrument is correspondingly oversized or the slit width is

reduced. Oversizing the spectrograph is impractical [for example,

each Gemini Multiobject Spectrograph (GMOS) weighs 2 tonnes

despite a modest collimated beam diameter of 100 mm]. Despite

the excellent image quality of modern telescopes, reducing the slit

width is only an option when observing point sources unless an

integral field unit or image slicer is used. We give examples of the

actual limits that this imposes in Section 2.

Immersed gratings allow this limit to be overcome. An immersed

grating is a conventional blazed reflection grating with a prism

optically coupled to the grating surface via a suitable medium. This

simple change has the potential to produce dramatic improvements

in resolving power, up to approximately a factor of 2 as shown in

Section 2.

Various ways of understanding why immersed gratings produce

this benefit have been presented by Wynne and Dekker, but the

simplest way of seeing this is to realize that the anamorphic

refraction introduced by the prism allows the length of the

illuminated grating, W, to be increased without requiring a

corresponding increase in the aperture of the camera which captures

the diffracted beam.

Although there have been many investigations of the advan-

tages of immersed gratings, very few devices have been employed

in visible-light spectrographs [however, see Dekker (1992) and

Diego et al. (1997)]. Two objections which have been cited are

that they involve an unacceptable drop in throughput and that they

produce ghost images. For these reasons, we have investigated the

properties of immersed gratings via experiments conducted on a

small laboratory prototype.

After reviewing the theory and presenting predictions for the

specific case of GMOS in Section 2.2, we present an experimental

verification of the theory in Section 3. In Section 4, we show

results of measurements of the grating efficiency, and in Section 5

we make a theoretical and experimental study of ghost images

produced by our immersed grating prototype. Our conclusions are

presented in Section 6.

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58 D. Lee and J. R. Allington-Smith

2 T H E O R E T I C A L BAC K G R O U N D A N D

P R E D I C T I O N S

2.1 Basic theory

Fig. 1 shows the layout of an immersed grating in a conventional

`blaze to camera' configuration.1 The prism (index nprism) is

attached to the grating surface via a medium (index ngap) while the

light enters from and exits into a medium of index n1. Normally

nprism � ngap and n1 � 1 (air). Light enters from the collimator (at

the left) and is refracted so that the beam intersects the grating

surface at an angle. The beam is diffracted by the grating and is

refracted by its second pass through the prism before exiting to the

camera. The result is a compression of the beam in the dispersion

direction compared with the case for a normal grating in this

configuration. The anamorphic factor is (Lee 1998)

A � Dcam

Dcoll

� cos d cos f cosb

cos g cos e cosa; �2�

where the angles are defined in Fig. 1 and are related by Snell's

law as

n1

nprism

� sinb

sina� sin g

sin d;

nprism

ngap

� sin i

sin e� sin u

sin f; �3�

and the prism vertex angle is f � e 2 b � f 2 g. Dcam and Dcoll

are the apertures of the collimator and camera respectively. The

anamorphic factor can be tuned by an appropriate choice of prism

to minimize the required aperture of the camera in the dispersion

direction.

Despite the compression of the output beam, the intersection of

the plane containing the grating surface with the incident beam, W,

can still be large, resulting in an increase in resolving power:

W � Dcoll cosb

cos e cosa: �4�

To calculate the resolving power, we start from the grating

equation applied in the immersing medium:

mrl � ngap�sin i 1 sin u�; �5�where i and u are the angles of incidence and diffraction at the

grating surface. We then differentiate with respect to the angle at

which diffracted light exits from the immersed grating, d , to

obtain the angular dispersion

dl

dd� n1 cos f cos d

mr cos g: �6�

The image of the slit width projected on the detector is

Dx � x f tel f cam

A f coll

; �7�

where ftel, fcam and fcoll are the focal lengths of the telescope,

camera and collimator respectively. Therefore the resolving power

(setting n1 � 1) is

R � l

Dl� l

dx

dl

� �1

Dx� l

dd

dl

� �f cam

Dx;

� mlr cosb

x cosa cos e

f coll

f tel

� mrlW

xDtel

: �8�

Thus the spectrograph still obeys the basic resolving power

equation (1), but the implicit increase in W allows the resolving

power to be increased. The expressions for R, W and �dl=dd� are

independent of the refractive index of the prism or immersing

medium. Note that we have ignored the dispersive effect of the

prism in the derivation of resolution in order to simplify the above

equations.

Detailed predictions of the ratio of illuminated grating lengths

(and hence the ratio of resolving powers) for the immersed and

unimmersed cases are presented in Section 2.2, where it is shown

that the ratio can reach factors of 2.

Another effect of immersion is that the blaze condition is

modified (Hulthen & Neuhaus 1954; Wynne 1989) so that the

blaze wavelength is approximately given by

lB < l 0Bngap; �9�

where l 0B is the unimmersed blaze wavelength.2 This can be

seen from equation (5) for constant input and output angles (i

and u ), or from equation (10).

Equivalently, the immersed grating behaves as an non-

immersed grating illuminated at wavelength l /ngap. This impor-

tant property allows longer wavelengths, or equivalently higher

ruling densities, to be used than in the unimmersed case. It also

permits the use of higher diffraction orders with the number of

observable orders proportional to ngap. This gives additional

flexibility in how immersed gratings may be used, resulting in the

potential for higher resolving power in addition to the purely

geometric factors discussed above.

The gains that can be achieved in the visible are surpassed in the

infrared region (Wiedemann & Jennings 1993; Graf et al. 1994),

where high refractive index infrared-transmitting materials are

available: e.g. silicon �n < 3:4� and germanium �n < 4�. This

permits significant gains in resolution to be achieved whilst the

costly infrared optics remain as small as possible.

Finally, we note that the anamorphic properties of an immersing

q 2000 RAS, MNRAS 312, 57±69

1

gap

prism

Blazed Grating Facets.(not to scale)

Immersi

on

medium.

e

n

n

n

Prism

θ

f

γ

δ

α

φ

φ

iβ

Figure 1. Schematic of an immersed grating. Dashed lines indicate the

normal to a surface. The solid line indicates the path of a ray.

1 This is the configuration used in conventional spectrographs which

maximizes grating length and hence resolving power. 2lB � l 0Bngap is true only for the Littrow configuration.

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An experimental investigation of immersed gratings 59

prism are also relevant for use with volume phase holographic

(VPH) gratings (Barden, Arns & Colburn 1998). As VPH gratings

can be produced with higher ruling densities than conventional

gratings, immersion allows access to longer wavelengths and

hence resolutions. The anamorphic properties of the prism can

also be used to reduce the beam deviation angle within the VPH,

leading to higher peak efficiency (a beam deviation of 908 has zero

efficiency in P-plane polarization).

2.2 Prediction for GMOS

To understand by how much the resolving power can be increased,

we need to make predictions for a particular grating geometry. We

take the example of the Gemini Multiobject Spectrographs

(GMOS: Allington-Smith et al. 1997; Murowinski et al. 1998)

which have a collimated beam diameter of Dcoll � 100 mm. We

have calculated the resolving power obtainable with slit width

x � 0:5 arcsec for a set of plane blazed reflection gratings

proposed at the Critical Design Review of the instruments, as

listed in Table 1 (also listed are the groove angle, j , often referred

to as the blaze angle, and the resolving power at blaze, RB, taking

into account the camera±collimator angle c � 508). In Fig. 2 we

show the predicted resolving power obtainable by tilting each

grating to different angles (a ) in first order. The width of each

trace indicates the simultaneous wavelength range (the length of

spectrum that is imaged on the detector surface at any one tilt

angle). The curves are terminated either when the efficiency of the

gratings is predicted to drop below 75 per cent of the blaze

efficiency (vertical limits) or when the camera is overfilled (the

upper horizontal limits). Note that all of these examples are based

on commercially available rulings. The use of gratings with other

rulings will permit any part of the parameter space to be

addressed.

This shows that the effective upper limit to the resolving power

is R < 5000 for x � 0:5 arcsec. Above this limit, the camera is

overfilled with a consequent reduction in throughput. The

resolution is not actually limited by overfilling of the camera

aperture. This is because vignetting of the pupil image is

equivalent to a reduction in the telescope aperture and hence a

corresponding increase in R from equation (1). Working in higher

order does not help because this increases �sin i 1 sin u� in

equation (5) which leads to overfilling of the camera even if the

interference condition can be satisfied. Note that ruling densities

r . 1200 mm21 cannot be used except at the very shortest

wavelengths.

We have also made predictions for immersed gratings as

detailed in Table 1 under the same constraints. Two of these make

use of ruling densities that would be impractical without

immersion. The refractive index of the immersing medium is

chosen to be 1.5. Immersion allows the maximum resolving power

to be greatly increased, by roughly a factor of 2. This would allow

GMOS to obtain twice the resolving power for the same slit width

or to operate with a slit twice as wide for the same resolving

power. An example of an application is the measurement of the

dark matter content of dwarf spheroidal galaxies in the Local

Group via estimation of the velocity dispersion obtained from the

radial velocities of individual stars. This requires R > 10 000 at

the wavelength of the calcium triplet which GMOS, equipped with

normal gratings, can only obtain by reducing the slit width to

< 0:25 arcsec. This restricts the project to rare conditions of

exquisite seeing. With the immersed grating illustrated (X2), the

project can be done with a slit width much better matched to

normal seeing conditions, leading to more efficient use of valuable

telescope time.

3 E X P E R I M E N TA L V E R I F I C AT I O N O F

I M M E R S E D G R AT I N G T H E O RY

Many publications have discussed the theoretical performance of

immersed gratings; however, there has been little experimental

work to verify the performance or efficiency of an immersed

grating. Whilst there is no reason to doubt that the theory is

correct, there may be some subtle effects that have been

overlooked. This section describes the manufacture and laboratory

testing of a prototype immersed grating. Further details regarding

construction and testing can be found in Lee (1998).

3.1 Construction of a prototype immersed grating

A small prototype immersed grating was constructed so that its

performance could be measured in laboratory tests. The prototype

consisted of a 308 BK7 prism optically coupled to the surface of a

1200 g mm21 diffraction grating (from Richardson Grating

Laboratory). The blaze angle of the grating is j � 218,corresponding to a blaze wavelength of 600 nm. The prototype

is therefore of a similar specification to an immersed grating

proposed for use with GMOS (see Table 1). Glycerol was used as

the coupling medium owing to its good index match with BK7

(nD � 1:473 for glycerol and 1.517 for BK7), and its ease of

removal by washing. As the glycerol remains liquid, the

immersing prism can be removed from the grating and re-applied

to allow different configurations of prism and grating to be

constructed. Also the absorption spectrum of glycerol does not

show any significant absorption in the wavelength region of

interest.

The assembled immersed grating can be seen in Fig. 3. It should

be noted that glycerol is not recommended for long-term use as an

immersing fluid, owing to its chemical reactivity.

3.2 Experimental procedure

The optical properties of the prototype immersed grating were

measured using a small bench-mounted spectrograph, as shown in

Fig. 4. Light from a sodium lamp passes through a variable

entrance slit, and is collimated by a plano-convex lens, dispersed

by the immersed grating, and re-imaged on to a CCD camera with

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Table 1. Gratings proposed for GMOS, andexamples of possible immersed gratings.

r j f lB RB

(mm21) (deg) (deg) (nm)

Unimmersed gratingsA 1200 17.5 0.0 463 3744B 831 19.7 0.0 757 4396C 600 8.6 0.0 461 1688D 600 17.5 0.0 926 3744H 400 9.7 0.0 764 1918IA 158 3.6 0.0 720 668

Immersed gratingsX1 2400 21.0 30.0 444 7043X2 1800 26.7 30.0 724 9572X3 1200 17.5 30.0 724 5372

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an achromatic camera lens. Images are captured with a frame

grabber and PC. The beamsize is set by a diaphragm to 10 mm to

reduce aberrations.3 The grating angle is set by an encoded

rotation stage.

The measured sodium D lamp spectrum consists of the two

bright sodium D lines, as seen in Fig. 5. The FWHM of the

spectral lines is determined by the input slit width and the

anamorphic magnification of the spectrograph as described in

Section 2.1. The dispersion of the grating can be determined from

the separation of the two D lines on the detector. The resolution4

and dispersion can therefore be measured from the recorded

spectrum.

3.3 Results

The experimental results are summarized in Table 2 together with

predictions made using the theory described in Section 2.1. The

angle of incidence at the prism is measured from the computerized

rotating stage when the spectrum is centred on the detector. The

estimated uncertainty is ^08: 02. The small discrepancy between

theory and experiment is consistent with a collimator-to-camera

angle of 458: 06, rather than the nominal 458, otherwise the angles

are in agreement with the theory. Small angular errors such as

these have a negligible effect on the other measured quantities.

The pixel scale on the detector is 12.35mm per pixel. The spectral

line FWHM can be measured to a precision of ^0:2 pixel. In all

cases the measured value is broader than the prediction, which is

consistent with a systematic error in the width of the entrance slit

for which the true width is 103mm, rather than the nominal

100mm.

The measurement uncertainty in the dispersion is ,0.5 per cent,

determined by the accuracy to which the centroid of the spectral

lines can be determined �^0:1 pixel�. The measured dispersion is

systematically larger than the predictions by an amount which is

consistent with the dispersion of the BK7 glass prism, which gives

,4 per cent extra dispersion.5

The measured resolution is in agreement with the predicted

value once the the systematic errors are removed. Exceptions are

the cases for m � 0 and 23 which show a large difference

between the measured and predicted image FWHM which lowers

the measured resolution. This is due to aberrations introduced by

the spectrograph at the large angles of operation required.

At the test wavelength, and in first order, the immersed grating

will still operate with an air gap present between the prism and the

grating. Table 2 shows that the performance is the same with or

without the prism immersed to the grating. This indicates that, as

expected, the plane-parallel medium between the prism and the

grating does not cause any dispersive effect. The air gap does,

however, introduce an additional air±glass reflection which causes

the ghost image seen in Fig. 5 (see Section 5). This ghost

q 2000 RAS, MNRAS 312, 57±69

Figure 2. Prediction of resolving power (0.5-arcsec slit) versus wavelength obtainable with the gratings listed in Table 1 with GMOS. The curves A, B, C, D,

H, IA refer to unimmersed gratings, while X1, X2 and X3 refer to immersed gratings. The blaze conditions are marked as solid dots. The width of each trace

in the wavelength direction indicates the maximum simultaneous wavelength range available with GMOS. The curves are terminated either when the

anamorphic factor exceeds 1.5 (horizontal limits) or when the efficiency is predicted to fall below 75 per cent of the blaze value (vertical limits) based on data

supplied by the grating manufacturer. The box indicates the parameter space required for the investigation of dark matter in Local Group dwarf spheroidal

galaxies described in the text. Only with immersed gratings can the goal of R . 10 000 be obtained with a reasonable slit width.

3 Limiting the beamsize to 10 mm has no effect on the resolution of the

optical system.4The Sparrow criterion (Hutley 1982) is used to define the resolution.

5 The additional dispersion of the immersing prism is described by Wynne

(1989), and may contribute a useful gain in an astronomical immersed

grating if high-dispersion prisms are used.

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disappears with immersion. It should be remembered that

operation at longer wavelengths and higher diffraction orders is

possible only with the use of immersion.

In summary, the prototype immersed grating behaves as

predicted by the theory presented in Section 2.1. No significant

deviations from the theory were observed within the experimental

errors. The theory of immersed gratings can therefore be used with

confidence.

4 M E A S U R E M E N T O F I M M E R S E D G R AT I N G

E F F I C I E N C Y

An important aspect of the performance of any dispersion system

is its efficiency, usually defined as the ratio of the amount of light

in the diffracted beam of interest to that in the incident beam.

Of the literature discussing immersed gratings (e.g. the papers

listed in Section 1), few present any efficiency data. The papers

that do present efficiency data give conflicting results. Dekker

(1992) and Wiedemann & Jennings (1993) both find that

unexplained efficiency losses occur when a grating is immersed.

Conversely, Radley et al. (1994) claim that the efficiency is not

significantly affected by immersion.

It is clear that a full investigation of the efficiency of immersed

gratings is required if the changes that occur with immersion are

to be understood. This section describes a series of measurements

performed on an immersed grating to characterize its efficiency

and investigate any loss mechanisms.

4.1 Theoretical expectations

Simple predictions regarding the efficiency of a diffraction grating

can be made using scalar theory. This assumes that geometrical

optics can be used to predict the behaviour of the incident and

diffracted beams. Scalar theory is limited to use in the regime

where lr , 0:2 and is therefore useful for predicting the

efficiency of echelle gratings (Schroeder & Hilliard 1980;

Szumski & Walker 1999). However, to predict the efficiency of

a finely ruled grating, a full electromagnetic wave solution has to

be performed. This takes account of the effects of polarization and

reflectivity. A full electromagnetic solution is beyond the scope of

this work. See Maystre, Neviere & Petit (1980), Loewen, Neviere

& Maystre (1977) and Hutley (1982) for more details regarding

the electromagnetic treatment of diffraction grating efficiencies.

Despite its limitations, scalar theory can be used to make a

number of predictions. The blaze wavelength, lB, is related to the

angle between the incident and diffracted rays, c , via

mrlB

ngap

� 2 sin j cosc

2; �10�

where j is the blaze angle of the grating (i.e. the angle between the

groove facets and the plane of the grating). The longest blaze

q 2000 RAS, MNRAS 312, 57±69

Figure 3. A photograph of the immersed grating taken during

manufacture. Note that the glycerol layer, visible at the top right-hand

corner of the prism, has yet to expand fully to the full area of the prism.

300 mm

Immersed grating210 mm

240 mm

CCD det

ecto

r

Light source baffle

Light source re-imaging

lens, focal length=120mm

Sodium D-lamp

Collimator lens

200 mm

Variable slit

Achro

mat

ic ca

mer

a len

s

Neutral density filter

Diaphragm

Grating rotation

Figure 4. Diagram of the bench spectrograph constructed to test the

properties of the prototype immersed grating.

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wavelength occurs in the Littrow configuration, and departure

from this reduces the blaze wavelength. It can also be shown

(Szumski & Walker 1999) that the blaze peak efficiency is

reduced as c is increased. This is an important result, because c is

reduced within the immersing prism, implying that an immersed

grating will have a higher efficiency at blaze than an non-

immersed grating.

4.2 Experimental procedure

The efficiency of a grating can be experimentally determined by

measuring the amount of light present in the diffracted beam and

comparing this with the amount of light in the incident beam. The

optical system constructed to perform this measurement is

illustrated in Fig. 6.

The output of the light source must remain constant while the

intensity in the incident and diffracted beams is measured,

otherwise the measured efficiency will be incorrect. To achieve

this a current-stabilized tungsten filament lamp was used,

providing constant illumination to within 0.5 per cent. Monochro-

matic light was produced by an Oriel monochromator. The

monochromator provides a quasi-monochromatic output with a

bandwidth of 5 nm at FWHM. An order-sorting filter was placed

in front of the monochromator to prevent the production of a

second-order spectrum which may produce errors in the

measurements. The monochromator allows the efficiency to be

measured anywhere in the wavelength range 400±1000 nm. The

output of the monochromator was collimated by a 200 mm focal

length plano-convex lens. A diaphragm was used to limit the beam

size to 10 mm.

A linear polarizing filter placed in the collimated beam allows

light polarized at any angle with respect to the grating rulings to

be produced. Unpolarized light is represented by light polarized at

458 with respect to the rulings. A Polaroid HN32 polarizing film

was used over the wavelength range 400±750 nm and an HR

polarizing film over the range 750±1000 nm.

The linearly polarized beam was then incident on the immersed

grating where diffraction occurs. The dispersed beam was imaged

on to the CCD detector by a 120 mm focal length plano-convex

lens. The grating efficiency can be measured with either c � 08(Littrow configuration) or c � 458. The Littrow configuration was

achieved by inserting a beam splitter into the collimated beam to

reflect the dispersed beam onto the camera arrangement, as

illustrated in Fig. 6. The extra reflection by the beam splitter in the

Littrow arrangement does not affect the measurement of

efficiency, although a brighter light source is needed to

compensate for the additional reflection losses.

The efficiency of the grating was measured in comparison with

a reference mirror. First the flux in the diffracted beam was

measured; the grating was then replaced with a reference mirror

and the reflected beam was measured. The ratio of the two

measurements gives the efficiency relative to the mirror. The

absolute efficiency can be found by correcting the relative

efficiency for the reflectivity of the reference mirror.

The flux present in the beam was determined from the image

captured by the CCD detector. First, the background level in the

image was determined and subtracted. The integrated flux in the

image of the monochromator slit could then be computed. Care

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Figure 5. Image and intensity cross-section of a sodium D spectrum

measured with the bench spectrograph and the immersed grating. Note the

fainter ghost image produced by reflection from the back surface of the

prism.

Table 2. Experimental results taken with the immersed grating.

nprism ngap m Angle a Image FWHM Dispersion Resolving power(deg) (mm) (nm/mm) (l /Dl)

theory expt theory expt theory expt theory expt

1.517 1.0a 21 3.80 3.79 175.2 176.5 2.11 2.04 1596 16361.517 1.0a 11 48.80 48.85 128.4 133.3 2.46 2.37 1865 18651.517 1.0a 21 3.80 3.81 175.2 178.1 2.11 2.03 1596 16301.517 1.0a 11 48.80 48.82 128.4 131.9 2.46 2.38 1865 18801.517 1.473 13 23.70 23.67 327.7 330.7 0.35 0.35 5074 50961.517 1.473 12 24.40 24.43 196.9 200.9 0.97 0.95 3087 30751.517 1.473 11 48.80 48.80 128.4 133.3 2.46 2.37 1865 18651.517 1.473 0 76.40 76.50 49.5 62.93 ¼ ¼ ¼ ¼1.517 1.473 21 3.80 ¼ 175.2 181.2 2.11 2.03 1596 16021.517 1.473 22 220.60 220.61 114.3 119.7 1.28 1.25 4046 39291.517 1.473 23 248.60 248.66 68.4 97.49 0.78 0.77 11044 7843

aThese measurements were taken with an air gap present between the prism and the grating.

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was taken to ensure that the detector was operated within its linear

range. The uncertainty in the measurement of grating efficiency

was estimated as ^1 per cent. Small variations in the light source

intensity and uncertainty in the background light level were the

major sources of error. The accuracy of the results has been

confirmed by the excellent agreement of efficiency measurements

taken many days apart.

4.3 Efficiency results

4.3.1 Blaze to collimator

The absolute efficiency of the immersed grating was measured

with a camera-to-collimator angle of 458 with blaze to collimator

and 458 polarized light. The efficiency of the unimmersed portion

of the grating was also measured with the same configuration. The

absolute efficiency curves are shown in Fig. 7. The size of the

symbols used in the plot represents the measurement uncer-

tainty. The efficiency curve supplied by the grating manufac-

turer, measured with c � 78: 5, is also plotted.

The manufacturer's data exhibit a blaze peak at 600 nm, in good

agreement with the value of 596 nm predicted via equation (10).

With c � 458 the position of the blaze peak is shifted to ,530 nm,

in reasonable agreement with the prediction of 552 nm. The peak

efficiency in the c � 458 configuration is reduced by ,5 per cent

compared with that in the c � 78: 5 configuration. This illustrates

the change in peak efficiency that occurs with changing

collimator-to-camera angle.

The immersed grating exhibits a blaze peak at approximately

800 nm. The position of the blaze peak is determined by the

wavelength within the immersing medium. A blaze peak at

800 nm corresponds to 540 nm in air. Therefore immersing the

grating shifts that blaze peak to longer wavelengths. Unfortu-

nately, the immersed blaze peak coincides with the aluminium

absorption feature at ,800 nm, somewhat disguising the shape of

the blaze peak. Note that a shift in the blaze peak will occur even

if the immersing medium is plane parallel (Hulthen & Neuhaus

1954). It is then possible to fine-tune the blaze wavelength, to suit

a certain astronomical application, by use of prisms of the

appropriate refractive indices in conjunction with gratings of

different blaze angle.

The Rayleigh passoff anomalies (Hutley 1982: indicated in

Fig. 7 with arrows) occur when the angle of diffraction is 908 and

the diffraction order skims the grating surface. The redistribution

of energy between the remaining diffraction orders, and electro-

magnetic coupling with the grating surface, causes discontinuities

in the efficiency curves. The wavelength at which an anomaly

occurs, la, is shifted to approximately nla in the immersing

medium, although a correction must be made to account for the

change in c within the immersing medium.

The main result is that efficiency is reduced with immersion.

The peak efficiency of the immersed grating is 15 per cent lower

than that of the unimmersed grating. Part of this loss, ,8 per cent,

can be attributed to Fresnel's reflection losses at the uncoated

surface of the prism. Fresnel's reflection losses arising from the

index mismatch between the prism and the immersing layer are

negligible. Absorption losses within the BK7 prism and the

immersing layer account for less than 0.1 per cent of the loss. The

remaining loss, ,7 per cent, is attributed to the reduction in

reflectivity of a metal surface when it is immersed (discussed in

Section 4.4). These results are similar to those previously reported

for an immersed echelle (Dekker 1992), although their loss

mechanism was unexplained.

4.3.2 Blaze to camera

The efficiency of the immersed grating was also measured in a

blaze-to-camera configuration for comparison with the previous

measurements. The efficiency was found to be essentially

identical with the blaze-to-collimator case within the experimental

errors (Lee 1998). This result indicates that losses owing to groove

shadowing are negligible, and that the immersed grating can be used

in either blaze-to-collimator or blaze-to-camera configurations

without any loss in efficiency.

4.3.3 Behaviour with polarization

The efficiency of the immersed grating was also measured with S-

and P-plane polarized light. P-plane polarized light has the

electric vector parallel with the grating rulings, and S-plane

polarized light has the electric vector perpendicular to the grating

rulings. The results for both c � 458 and Littrow configurations

are shown in Fig. 8.

It should be noted that anomalies only occur with S-plane

polarized light. The P-plane peak efficiency is lower than with S-

plane polarized light. The S-plane efficiency continues to increase

with increasing wavelength, after the P-plane efficiency has begun

to decrease, reaching ,90 per cent relative efficiency. Gratings

with blaze angles around 218 are well known for their wide S-

plane efficiency performance (Loewen et al. 1977).

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Neutral density filter

Collimator lens

Diaphragm

Polarizing filter

Order sorting filter

Stabalized Tungsten lamp

Optional Littrow

beam splitter

CCD det

ecto

r

Camer

a len

s

200 mm

120 mm

Immersed grating

Monochromator

210 mm

240 mm

Exit slit

Entrance slit

camera arrangementAlternative Littrow efficiency

Figure 6. Diagram of the bench spectrograph constructed to measure the

efficiency of the prototype immersed grating.

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For a grating in Littrow configuration, when the inequality

lr . 2=3 is satisfied, only diffraction orders m � 0 and 1 can

propagate. High efficiency can therefore be expected as a minimum

of light is lost into other orders. It can also be shown via the

reciprocity theorem (Maystre et al. 1980) that for a sufficiently

finely ruled grating with j . 198: 5 (i.e. lB . 556:3 nm for

r � 1200 g mm21�, in S-plane polarized light, a first-order effi-

ciency can be achieved which is limited only by the reflectivity of

the grating surface. This explains the region of high efficiency in

the immersed S-plane efficiency curve with l . 820 nm.

S-plane polarized light that enters the prism at Brewster's angle

(typically a , 608) does not suffer any reflection loss. The large

angle of incidence with the prism implies a large anamorphic

effect and hence high resolution (Dekker 1987). This property

coupled with the efficiency behaviour described above leads to

the possibility of constructing a highly efficient, high spectral

resolution dispersion system which operates in S-plane polarized

light. A polarizing beam splitter and wave-plate would be required

to convert the incident P-plane light to S-plane polarization,

implying dual-beam operation. This type of dispersion element

may therefore be suitable for use in a spectropolarimeter.

4.3.4 Littrow configuration

A direct comparison of efficiency between immersed and

unimmersed gratings in a non-Littrow configuration is made

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olut

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Unimmersed grating 45PolarisationImmersed grating 45PolarisationManufacturers data

Unimmersed blaze peak Immersed blaze peak

Figure 7. Comparison of absolute efficiency curves in immersed and unimmersed configurations with c � 458 and polarization of 458. Also shown is the

efficiency curve taken from the manufacturer's data sheet with c � 78: 5. Grating anomalies are indicated with a small vertical arrow.

500.0 600.0 700.0 800.0 900.0 1000.0Wavelength (nm)

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Immersed grating Pplane (psi=45)Immersed grating Splane (psi=45)Immersed grating Pplane (Littrow)Immersed grating Splane (Littrow)

Figure 8. Plot of relative efficiency for the immersed grating in both S-plane and P-plane polarizations. The efficiency curves corresponding to c � 458 and

Littrow configuration �c � 08� are shown. Note the shift in position of the S-plane anomaly, from ,800 to ,650 nm, with changing collimator-to-camera

angle, and the change in the P-plane blaze peak.

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difficult by the change in the effective collimator±camera angle,

c , within the prism. Immersion reduces c from 458 to 288 which

produces an increase in the peak efficiency of ,5 per cent.6

However, the Littrow configuration allows a more direct compari-

son of efficiencies as c � 08 in both immersed and non-immersed

cases. The results for this configuration can be seen in Fig. 9.

The efficiency of the immersed grating at wavelength l can

now be directly compared with the equivalent unimmersed

efficiency at l /ngap. The immersed grating efficiency curve in

Fig. 9 has been shifted in wavelength to allow this comparison to

be made more easily. The ratio of immersed to unimmersed

efficiency, corrected to remove the effect of Fresnel's reflection

losses, is plotted in Fig. 10.

The ratio of efficiencies shows that the absolute efficiency with

immersion can be up to ,12 per cent lower than in the

unimmersed case. However, at some wavelengths the immersed

efficiency can actually be higher. If it is assumed that complex

electromagnetic effects can be ignored, then the ratio of

efficiencies is simply related to the ratio of reflectivities of the

metal surface at the two wavelengths being compared, assuming

that the reflectivity of the grating facet is the same as that of bulk

aluminium. The resulting reflectivity ratio of an immersed

aluminium surface compared with a unimmersed surface is also

plotted in Fig. 10 using data from Hunter (1985) and the theory in

Section 4.4. It can be seen that the P-plane efficiency ratio is

reasonably well fitted by the prediction. This might be expected,

since it is P-plane behaviour that is most closely predicted by

scalar theory. However, the S-plane efficiency ratio is higher than

expected from the theory.

Clearly the assumption that complex electromagnetic inter-

actions can be ignored is risky, especially as the wavelength is

only a factor of 2 smaller than the groove size. This result

indicates that the reduction in efficiency of an immersed grating

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olut

e ef

ficie

ncy

unimmersed PplaneImmersed Pplane (wavelength shifted)unimmersed SplaneImmersed Splane (wavelength shifted)Immersed SplaneImmersed Pplane

Figure 9. Plot of absolute efficiency curves obtained in the Littrow configuration for both the immersed and unimmersed gratings. Curves for both S- and P-

plane polarizations are shown. The immersed grating efficiency curves have also been shifted in wavelength, by dividing by the refractive index of the

immersing medium, for direct comparison with the unimmersed grating data. Note that the positions of the S-plane immersed and unimmersed anomalies

coincide in the Littrow configuration.

Figure 10. Plot to show the ratio of immersed and non-immersed grating

absolute efficiency curves in the Littrow configuration. The ratio has been

corrected to remove the effect of air±glass losses at the prism surface. Also

shown is the theoretical prediction obtained from the change in reflectivity

of an immersed aluminium surface.

6 The increase in efficiency is estimated from the published efficiency

curves in Loewen et al. (1977).

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may be related, in P-plane polarization, to the drop in

efficiency of an immersed metal surface. The S-plane ratio

shows an improvement in efficiency for a small portion of the

blaze profile. This indicates that for certain conditions it may be

possible to achieve higher efficiencies with immersion.

The anomaly at 819 nm, or equivalently 556 nm in air, is caused

by spectral orders m � 21 and 2 being diffracted at u � 908. The

depth of this anomaly is unchanged by immersion (there is no

sharp deviation in the ratio of efficiencies), indicating that

immersion does not have a significant effect on the strength of

anomalies.

4.4 Metal±dielectric losses

The decrease in efficiency of an immersed grating is partly caused

by metal±dielectric losses. Reflection losses that occur at an air±

glass interface are well known. It is, however, less well known that

a reduction in reflectivity occurs when a metal surface is

immersed. The refractive index of a metal surface can be

represented by a complex number (Jenkins & White 1976):

nc � nR 1 inI; �11�where nR is the real refractive index and nI is the imaginary

refractive index. The real refractive index behaves as an ordinary

refractive index, determining the wave speed in the material, and

the imaginary refractive index behaves as an extinction coeffi-

cient, determining the rate of absorption in the material (Pedrotti

& Pedrotti 1993). The refractive index coefficients are frequency-

dependent and are therefore unaltered by the change in wavelength

that occurs in the immersing medium.

A derivation of the reflectivity of a metal surface, in S- and P-

plane polarizations, can be found in most introductory optics texts

(e.g. Fowles 1989). For normal incidence the following simplified

formula can be derived:

R � �ngap 2 nR�2 1 n2I

�ngap 1 nR�2 1 n2I

; �12�

where R is the reflectivity of the immersed metal surface. To

illustrate this effect the reduction in reflectivity of an aluminium

mirror, upon immersion within a medium of refractive index 1.5,

is shown in Fig. 11. Refractive index data for aluminium are taken

from Hunter (1985). The reduction in reflectivity is generally

around 4 per cent, although this will depend critically on the actual

properties of the immersed metal surface. Metal±dielectric losses

increase with the refractive index of the immersing medium. In the

case with nI � 0 (a perfect dielectric), equation (12) reduces to the

well-known formula for Fresnel's reflection from a glass surface.

Accurate prediction of the metal±dielectric loss at the grating

surface would require knowledge of the complex refractive index

of the grating coating, and a full electromagnetic solution. The

measured metal±dielectric loss of ,7 per cent is consistent with

the reflectivity predicted using equation (12), as shown in Fig. 10.

This lends support to the assumption that the reflectivity of the

immersed grating facet can be approximated by the reflectivity of

bulk aluminium immersed in glass.

Although immersing a grating leads, initially, to a small reduction

in efficiency, the prism also protects the grating from damage and

contamination. The efficiency of a bare grating reduces with time

owing to contamination and oxidation. Immersion might be

expected to preserve the reflectivity of the grating surface. It is

also straightforward to clean the prism. Immersion might therefore

be useful to protect gratings used in extreme environments, such

as in the vacuum ultraviolet.

5 G H O S T I M AG E S

5.1 Predictions

Stray reflections within the spectrograph, particularly those that

occur within the collimated space, may be focused on the detector

to form ghost images.7 The probability of producing a ghost image

is higher for an immersed grating because of the extra air±glass

surface and the increased number of diffraction orders that can

propagate.

An example of ghost formation within an immersed grating is

illustrated in Fig. 12. Light at 617 nm enters the immersed grating

and is diffracted in second order back towards the incident beam.

q 2000 RAS, MNRAS 312, 57±69

Figure 11. Plot of the reflectivity of an aluminium surface versus

wavelength for unpolarized light. The angle between the incident and

reflected beams is 458.

Input Beam

Output Beams

PRISM

prism surface.Ghost reflections at

Diffraction Gratingimmersed to prism.

Figure 12. Schematic of the production of an immersed grating ghost. The

configuration shown is for the prototype immersed grating operating at a

wavelength of 589 nm. A ghost occurs at 617 nm owing to second-order

diffraction, followed by reflection from the prism surface, followed by

first-order diffraction.

7 Grating ghosts, caused by ruling defects, may also occur but are not

considered here.

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The beam is reflected by the surface of the prism and is then

diffracted in first order to produce a ghost image in the same

location as the first-order image. Ghosts can also be produced by

reflections from other reflective surfaces in the optical system

such as the entrance slit or detector surface.

Ghosts that are caused by the immersing prism occur over a

wide range of wavelengths and diffraction orders. Theoretical

predictions of the occurrence of ghosts for the prototype immersed

grating are shown in Fig. 13. The plot shows the predicted

wavelength, lg, at which the ghost occurs, versus the central

wavelength of the observation. In cases where the ghosts are

produced with high diffraction orders the surface brightness is

likely to be low because of the high dispersion. The intensity of

ghosts is also reduced somewhat by vignetting. The optical path of

the ghost within the prism produces an offset of the ghost beam

from the centre of the camera axis, leading to vignetting. Many

ghosts can be avoided completely by the use of suitable bandpass

or order-sorting filters to limit the wavelength range incident on

the grating. Ghosts incident on the prism surface at sufficiently

large angles will undergo total internal reflection and become

trapped within the prism. Whilst these ghosts do not reach the

detector, they may contribute to an increase in the total intensity of

stray or diffuse background light.

5.2 Measurement of ghost intensity

The presence of ghost images could be a serious problem for

certain observational programmes, preventing the use of an

immersed grating. We therefore decided to measure the intensity

of ghost images produced by the prototype immersed grating. The

experimental setup shown in Fig. 6 was used to capture images of

the parent line and the ghost. As both the ghost and the parent are

captured on the same image, it is straightforward to measure the

relative intensity of the ghost image. A science-grade cooled CCD

camera was used to capture the images because of the need for

low read noise and high dynamic range.

An example of a ghost image is shown in Fig. 14. This is the

ghost produced by the optical path illustrated in Fig. 12. Results

for the relative intensities of various ghosts are listed in Table 3.

The brightest prism ghost measured has an integrated intensity of

1.3 per cent relative to the parent image. The peak intensity of the

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host

imag

e (n

m)

ghost order (1,2)ghost order (2,1)ghost order (0,3)ghost order (1,1)ghost order (0,2)central wavelength = ghost wavelength

Figure 13. Graph of wavelength at which an air±glass surface prism ghost will appear, versus central wavelength. For example, with a central wavelength of

600 nm, ghosts will occur at 561, 564, 621, 840 and 903 nm, caused by the various grating orders listed in the key to the figure.

Figure 14. Image of an immersed grating ghost, at 617 nm, caused by first-

order diffraction, then Fresnel reflection within the immersing prism, and

finally second-order diffraction. The ghost is the faint dispersed image.

The `parent' image is the black area (black because of scaling) to the right

of the image. The integrated ghost intensity is less than 1 per cent of that of

the parent in unpolarized light.

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ghost is only 0.34 per cent of the parent image, owing to the high

dispersion of the ghost. Note that ghost reflections at the prism

surface are suppressed in transverse magnetic polarization near to

Brewster's angle. By far the brightest ghosts found were those

arising from reflections between the CCD detector and other

components in the optical system.

The specification regarding ghost intensities for GMOS states

that: `No single localised parasitic image shall have a surface

brightness exceeding 2% of the field illumination for any 100 nm

bandpass in the design range (assuming a typical CCD and

dewar).' The prototype immersed grating performs within this

specification even without the use of antireflection coatings. This

implies that the production of bright ghost images is not a major

disadvantage with the use of immersed gratings.

Of course, the intensity of prism ghosts will be significantly

reduced by the use of suitable antireflection coatings on the

surface of the prism. Ghosts can also be deflected away from the

camera axis by tilting the input face of the prism with respect to

the camera axis. Unfortunately, this also introduces a small

amount of cross-dispersion into the system. This is not a problem

if the immersing prism is also the first prism in a cross-dispersion

system, as is the case with the HROS immersed echelle (Radley

et al. 1994).

6 C O N C L U S I O N S

The factors that limit the maximum attainable resolution of an

astronomical spectrograph have been discussed, in particular the

decrease in resolution with increasing telescope aperture.

Immersed gratings offer a way of compensating for this. The

theory of immersed gratings has been presented with particular

attention to the resolution gains that are possible. Predictions for

GMOS show that immersed gratings may allow the spectral

resolution to be approximately doubled without additional

throughput loss by vignetting.

The theory of immersed gratings has been verified by construc-

tion and testing of a small laboratory prototype. The prototype

immersed grating performed exactly as predicted by the theory.

The efficiency of the immersed grating has also been measured

and found to be up to ,15 per cent lower than that of the same

grating in air. This reduction in efficiency is attributed to two main

causes:

(i) air±glass reflection losses at the uncoated surfaces of the

prism;

(ii) metal±dielectric losses owing to the reduction in reflectivity

of an immersed metal surface.

The effect of the metal±dielectric losses, in certain circum-

stances, is somewhat offset by the gain in efficiency owing to the

reduction in collimator-to-camera angle within the immersing

medium. The position of the blaze peak is shifted by immersion by

a factor approximately equal to the refractive index of the

immersing medium.

The intensity of ghosts produced by reflections from the prism

has also been measured. They are found to be faint, even without

antireflection coatings on the prism, with a peak intensity less than

0.4 per cent of that in the parent image, which is consistent with

the stated requirements of GMOS.

Finally, we discuss the prospects for the manufacture of

large astronomical immersed gratings. The extra weight of the

prism, and the need to maintain stability during high-resolution

observations, will require development of suitable support

structures. Prism glasses will need to be procured in large sizes,

with appropriate homogeneity to reduce wavefront distortions, and

low bubble and exclusion content to reduce scattered light. Similar

arguments apply to the immersing medium. There is a choice of

methods to manufacture the immersed grating: for example, the

separate components could be optically coupled using an

appropriate medium, or the grating could be directly ruled on to

the prism. It will also be worth investigating the use of

antireflection coatings, since the requirement to work over large

angles may rule out the use of interference coatings.

The general conclusion of our work is that the minor

disadvantages of using an immersed grating are more than offset

by the significant gains that immersion has to offer. It is hoped

that this paper has clearly demonstrated the advantages of using

immersed gratings, and removed uncertainties associated with

their performance.

AC K N OW L E D G M E N T S

We thank colleagues in Durham for their assistance with this

work, in particular George Dodsworth, Roger Haynes, John

Webster, Pete Doel, Colin Dunlop and the members of the

mechanical workshop. We also thank Charles Wynne for drawing

our attention to the potential of immersed gratings and, many

years ago, suggesting an experimental investigation. We thank the

Particle Physics and Astronomy Research Council for their

financial support of this work and DL's studentship.

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Table 3. Measured intensities of ghost images.

lg (nm) Order RTMa RTE

a ITMb ITE

b

617 (21,2 2) 0.043 0.043 0.012 0.0060558 (22,2 1) 0.000 0.125 ¼ 0.0134562 (0,2 3) 0.005 0.120 ¼ 0.0060600c (21,2 2) 0.300d 0.300d 0.0362 0.0147

aRTM and RTE are the reflectivities of the prism surface for thetwo polarization states. In some cases the low reflectivity of theprism surface makes the ghost undetectable.bITM and ITE are measured ghost intensities, relative to theparent image, for the two polarization states.cIndicates a CCD detector reflection ghost, not a prism ghost.dEstimated value of the reflectivity of the CCD at 600 nm atnormal incidence. D

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This paper has been typeset from a TEX/LATEX file prepared by the author.

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An experimental investigation of immersed gratings