Submitted to Publ. Astr. Soc. Pac.
Parallelism of a Fabry-Perot Cavity at Micron Spacings
D. Heath Jones
1
and Joss Bland-Hawthorn
2
ABSTRACT
We describe a method to quantify the degree of parallelism between two transparent
glass mirrors spaced a few microns apart. Our technique, which permits measurement
and correction of deviations as small as =10000 from parallelism, is fundamental to
the successful operation of tunable narrowband interference lters for two reasons.
First, the highest throughput is achieved when the plates are parallel at any plate
spacing. Secondly, the lowest resolution (largest bandpass) imaging is achieved when
the plates are only a few microns apart but there is a real danger of the plates touching
if parallelism is not maintained.
The TAURUS Tunable Filter (TTF3) is a Fabry-Perot cavity with an adjustable
plate spacing of 2 to 13 m. The parallelism measurement involves repeated imaging
through a focal plane slit and a series of pupil plane masks. This approach is
particularly ecient when the plate scanning is synchronized with movement of charge
on the CCD. We assess the eects of wavelength-dependent phase changes within the
inner surface coatings of the plates. These become important as the plates approach a
spacing comparable in size to the thickness of the coatings.
Subject headings: instrumentation: Fabry-Perot interferometers | detectors:
charge-coupled devices
1 Mount
Stromlo and Siding Spring Observatories
Private Bag, Weston Creek P.O., ACT 2611, Australia
E-mail: [email protected]
2 Anglo-Australian Observatory,
P.O. Box 296, Epping NSW 2121, Australia
E-mail: [email protected]
3 The TTF comprises a blue and a red lter with wavelength coverage 370{650 nm and 630{960 nm.
{2{
1. Introduction
Fabry-Perot interferometers have long been used in astronomy as a means of obtaining
narrowband imaging of galaxies and nebulae (q.v. Bland-Hawthorn 1995). However, with typical
plate spacings in the range 20 to 500 m, optical instruments have been conned to high
orders of interference (m 50 to 2000). Most work is therefore restricted to relatively high
resolution (= > 1500) where the interference rings are narrow and cover only a small area on
the detector. For astronomical work, the drawback of this type of imaging is that interference
regions consequently cover only a small solid angle on the sky.
To solve this problem, we have successfully commissioned a narrow-gap Fabry-Perot
interferometer called the Taurus Tunable Filter (TTF; Bland-Hawthorn & Jones 1998), based on a
design originated by Atherton & Reay (1981). This lter consists of two parallel glass plates with
an adjustable gap spacing of 2 to 13 m. Two recent advancements have led to the development
of this instrument. First, multilayer dielectric coatings are now able to cover 300 nm or more with
transmissions of 99% or better. Secondly, it is now possible to drive Fabry-Perots to gap spacings
as small as 1 m which requires that the cavity spacing be kept clean of even a single dust speck.
The dynamic range of accessible plate spacings is much broader than earlier instruments due
to developments in stacked piezo-electric transducers (PZTs). These permit the TTF to scan
through a range of spacings four times larger than that accessible by conventional Fabry-Perot
spectrometers. Unlike the instrument of Atherton & Reay (1981), the TTF coatings of each
surface are polished to a atness better than =140 (post coating) and optimised for 300 nm
wavelength coverage for both the red and blue arms. The tunable lter is used in conjunction with
high performance, large format (e.g. MIT-LL 2048 4096) CCDs. Alternative tunable devices
such as acousto-optic or birefringent lters do not currently match the qualities that make the
Fabry-Perot system most desirable for astronomical imaging (Bland-Hawthorn & Cecil 1996).
The combination of moderate telescope f -ratio (f=8) and narrow gap spacing of TTF
means that the requirement for large-area interference is met. However, ensuring parallelism
of the plates becomes increasingly critical at the limit of narrow spacings. For conventional
instruments, parallelism can be judged by eye according to how stable the interference rings from
a monochromatic source remain with changes in viewing position. This approach works well at
visible wavelengths for Fabry-Perots with widely spaced plates. For plates that are narrowly
separated, the order of interference is too low (typically m < 20) and since the eld is essentially
monochromatic, it fails to provide the sharp rings necessary for visual assessment over a light
table.
To overcome this we have developed a test that eciently optimises plate parallelism up to
=10000. This limit is dened by the smallest deviation that we can both measure and correct,
as derived in Sect. 3.2. Our test is eective over the full range of TTF spacings down to 2 m.
Alternative techniques for measuring parallelism, such as beam partitioning by insect-eye lenses
(Meaburn et al. 1976), were explored and found impracticable for an astronomical imager such
{3{
as TTF. A novel CCD charge-shuing technique is employed that involves multiply exposing a
single CCD image during the test. This avoids the need to produce many separate CCD images.
At the narrowest spacings we are in a regime where deviations from phase change upon
reectance are important. This occurs as the gap size becomes comparable with the thickness of the
inner optical coatings. Each 16-layer dielectric has a total thickness of 1.55 m. Non-uniformities
in the coating structure also become apparent as the plate spacing approaches this limit. In
particular, the interference fringes deviate from circular symmetry. We calculate the eects of this
phenomenon across scans at the narrow-gap limit of our instrument. The wavelength-dependent
phase changes and non-uniformities are negligible at large gap.
The paper here is organised as follows. The experiment layout and operation are detailed
in Sect. 2. A description of the parallelism test is given in Sect. 3, including the eect of phase
changes within the plate coatings. Section 4 contains concluding remarks.
2. Set-Up and Operation
2.1. Charge Shuing
Charge shuing is the ability to multiply expose and shift an individual CCD frame backwards
and forwards along the chip many times before read out. With the AAO-1 controller and a
MIT-LL CCD, a single row of 2048 pixels can be shued one row in 50 s whereas to read out
the same row takes 40 ms. This technique has been used with TAURUS at the Anglo-Australian
Observatory since 1994.
Charge shuing is essential to eective parallelism testing as it provides a powerful tool for
sampling TTF throughput as it is stepped over successive gap spacings, without the need for
many discrete CCD images. Similar charge shuing methods have been applied to other forms of
astronomical imaging such as imaging polarimetry (Clemens & Leach 1987) and spectroscopy of
faint galaxies (Cuillandre et al. 1994). Bland-Hawthorn & Jones (1998) describe more sophisticated
charge shue applications with TTF.
We use both the MIT-LL 4096 2048 (rows columns) CCD with 15 m pixels and
a 1024 1024 Tektronix CCD with 24 m pixels. Both are buried-channel devices with
charge-transfer eciencies (CTEs) in excess of 0.99999. Tests involving repeated shuing with
the Tektronix chip have demonstrated that 100 full-frame shues are possible before signicant
charge-loss occurs (Bland-Hawthorn & Jones 1998). Bulk traps are the major cause of charge
loss, arising from impurities and defects within the silicon lattice of the CCD (Janesick & Elliott
1992). The missing charge leaks out of trailing pixels as a deferred charge or is lost through
recombination. The TTF plate spacing can be also be changed and allowed to settle within the
time of a single shue (50 s). The primary limitation to shue speed is the shutter, which keeps
{4{
the rate at 1 s for one complete shue.
2.2. Pupil Hartmann test
The parallelism test employs an identical optical arrangement to that for astronomical
imaging, with the exception of masks added at the focal and pupil planes. Figure 1 shows the
main components of the system. Our basic method is to irradiate the TTF with a monochromatic
source. In the focal plane, we use a slit which projects to a few rows of the CCD. The slit mask
ensures that only a thin strip of monochromatic light is imaged at the centre of the CCD detector.
The tunable lter is located in a collimated beam and quadrant-shaped masks placed in the pupil
plane isolate a quarter of the TTF plate area at a time for testing.
The long-slit spectra used for determining parallelism are obtained in the following manner.
An exposure is taken, at the end of which the shutter is closed, the TTF plates shift to the next
value of plate spacing and the current frame in the CCD is shifted by a small amount. The shutter
is then re-opened for the next exposure, sampling the light source at the new spacing. The CCD
is multiply-exposed 100?200 times before it is eventually read out. This produces a long-slit
spectrum similar in appearance to that obtained from a grating spectrograph. The method can
be sped up by keeping the shutter open and shuing the charge during the exposure. But a
signicant time constant, which determines the settle time of the plates, can lead to a spurious
phase oset.
Figure 2 shows an example of a long-slit spectrum of a Cu-Ar lamp obtained using the red
TTF and charge shuing with the Tektronix CCD. The spectrum covers 730-788 nm and
comprises 80 discrete shue exposures, only covering the top half of the CCD. This is because a
fraction (n ? 1)=(2n ? 1) of the detector area must be sacriced in a shue of n rows to allow
space for the spectrum to be shued along as it is built. The lines are narrow because the TTF
was set to a large gap (12 m). The curvature of the lines is due to the combined eects of radial
phase change and scan increment. It is emphasised at large gap (higher orders of interference) or
when small increments in spacing are used between successive shues. Once parallelism has been
established at large spacing, the plates retain their alignment irrespective of how TTF is tuned
thereafter.
As shuing is ordered top-to-bottom, the row number on the image is linearly related
to increasing gap spacing between the plates. However, this does not necessarily imply that
wavelength is strictly increasing over a full shue. Occasionally wavelength wrap-around occurs
between adjacent orders of interference. To remove this confusion, we typically observe through
two orders of interference.
2.3. Control of TTF Plates
{5{
For peak performance of a Fabry-Perot device the error in plate parallelism must be much
less than deviations from atness in the plate surface. The coated plates in TTF are individually
at to =140 and normally parallelism must be established and maintained to at least =500
during use. To achieve this, the plates of TTF are controlled through an active feedback loop that
constantly corrects the plates when small changes from plate position occur (Hicks & Atherton
1997; q.v. Ramsay 1962). Such closed loop control is essential for a device such as TTF, where
plate stability could otherwise be inuenced by variations in temperature, humidity and gravity
on the plates as the telescope moves.
Hicks, Reay & Atherton (1984) pioneered the technique of Fabry-Perot stabilization using a
capacitance bridge. Their Fig. 1 shows the components employed in the active feedback system
used by TTF. Four capacitors around the edge of the inner plate surfaces (labelled in their Fig. 1
as CX1, CX2 , CY1 and CY2 ) detect changes in plate spacing. Such changes permit measurement
of the plate tilt along the direction of the x-y axes dened by the two capacitor pairs. This
capacitance micrometry is capable of detecting displacements of 10?12 m (Jones & Richards 1973).
Tilt information from the capacitors is fed to piezo-electric transducers (PZTs) which compensate
for the amount of deviation. There are three PZTs, each located around the plate edge between
the capacitors and separated by 120. An additional reference capacitor measures the gap spacing
with respect to a xed capacitor built onto one of the plates.
When the plates are parallel, capacitance will not be equal between either the CX1, CX2 or
CY1 , CY2 pairs. This is why the feedback system can only maintain parallelism and not establish
it in the rst place. Electronic osets are applied to compensate for variations in capacitance
whenever they occur. These can arise from temperature gradients across the Fabry-Perot or
continual changes in the piezo dimensions due to creep in the PZT lattice structure. All such
capactitance changes are continually balanced and nulled automatically by the system electronics.
We are able to introduce xed vertical osets ZX , ZY , along the x and y directions through
three levels of control: coarse, ne and software. Both coarse and ne are analogue inputs directly
through the hardware of the TTF controller. Software control allows precision adjustment of the
plates via digital input. The maximum ZX and ZY amplitudes are 3.21 m. Clearly, it is crucial
to ensure the plates are parallel before attempting to achieve gaps smaller than about 7m. The
vertical deviation along the x-axis from the zero-point is given by
ZX = 0:2Xc + 0:021Xf + Xs =4096
(1)
where ZX is in microns and Xc , Xf and Xs are the respective coarse, ne and software settings
in X . Each control has its own range: Xc 2 [?5; +5], Xf 2 [0; 10] and Xs 2 [?2048; +2048]. An
identical calibration relates ZY with Yc , Yf and Ys , across identical settings.
No gap scanning is done through the ZX or ZY movements. They are purely osets that
remain xed unless adjusted for parallelism. Scanning is controlled through a third parameter Z
which has the much larger amplitude of 13.05 m. It too can be adjusted through three levels of
{6{
coarse, ne and software control,
Z = Zc + 0:105Zf + Zs =2048 + 5:488;
(2)
although with a much larger range in the coarse setting than ZX or ZY . Equation (2) is
the absolute calibration used to tune the plates to arbitrary gap (and therefore wavelength)
during normal observing. It depends on the values of (Xc; Xf ; Xs) and (Yc ; Yf ; Ys ) at the
time of calibration; in the case of Eqn. (2), for the TTF, (Xc ; Xf ; Xs) = (0:0; 3:90; 0:0) and
(Yc ; Yf ; Ys ) = (0:1; 8:00; 0:0). Although the setting limits of Zc , Zf and Zs are identical to those
of x and y , the corresponding physical ranges are much larger. Since Zc and Zf are analogue
controls, all gap scanning is done through automated stepping of Zs in software. The units of Z
in Eqn. (2) are microns.
The amount of oset is derived directly from the parallelism test and rened through
successive iterations. We describe the test in the following section.
3. Parallelism Test
3.1. Method
The X -Y capacitive bridges dene the direction of the orthogonal x and y axes. We assume
that all components are located centrally to the beam although this alignment is not critical. Only
three of the four possible quadrants are needed to establish magnitude and direction of plate tilt.
In any such arrangement of quadrants, we dene the corner quadrant to be the reference quadrant
and the remaining pair as the X and Y quadrants according to their direction from the reference.
We image an emission line by scanning through each quadrant in turn, producing a
charge-shued long-slit spectrum for each. The amount of tilt is measured by the size of the oset
between the line through the X or Y and the reference quadrant. The plates are parallel when no
osets exist in either direction and the emission line appears simultaneously in all three.
Figure 3 shows how adjustment of the capacitive osets optimises plate separation. Here,
identical central strips have been taken from a full charge-shue image (such as Fig. 2). The X ,
Y and reference quadrants are labelled. Each shue step represents an increase in plate spacing
of 8 A or =1140. Panel (a) shows a small oset in Y only (arrowed). This implies the plates
are tilted in the y -direction but not that of x. In the following section we demonstrate how this
oset in gap is proportional to the osets input to compensate. Note that the calibration source
seen in Fig. 3 is poorly diused over the entrance aperture and dierences in illumination between
quadrants are present.
Panel (b) shows the appearance of the lines when the plates are more poorly aligned. Not
only are the lines misaligned in this case but much less distinct as well. Preliminary adjustments
{7{
such as those between (a) and (b) are used to establish the directional relationship between oset
voltage and tilt. Having the pupil masks telecentric with quadrant edges aligned to the x-y axes
greatly simplies the process.
The remaining ne adjustment of the plates is an iterative process whereby piezo oset
voltages are adjusted through software control until the wavelength osets between all quadrants
are zero. Alignment of all lines in (c) indicates the plates to be parallel. This ensures that the
eective nesse and throughput of the instrument are now optimised.
3.2. Deriving a Corrective Oset
We now derive the relationship between a directional oset (as measured optically near the
centres of each quadrant) and the corrective oset (as applies in the vicinity of the capacitors and
PZTs). This is necessary because the osets for a tilted plate are measured and corrected in two
dierent locations, namely, the centre and edge of the plate respectively.
Suppose the upper plate is tilted along the plane
z(x; y) = L0 ? Ax ? By
(3)
relative to the lower plate at z (x; y ) = 0. Here, L0 is the separation of the plate centres (in m)
and A and B are constants proportional to slope in x and y . We assume that the x ? y axes align
with the XY capacitors and that p ? q axes dene the four segments of the pupil plane masks.
Initially we also assume the p ? q axes to be rotated an angle counter-clockwise from the positive
x-axis.
The location of emission-lines (such as those in Fig. 3) determines the eective plate separation
over that region. The eective plate separation is the volume of space between the plates divided
by the cross-sectional beam area isolated by the quadrant mask. Integrating over each quadrant
in turn gives eective plate separations
RRR
dV = L ? 4Rp h(pA + qB) cos + (?qA + pB) sin i;
(4)
L(p;q) = RR dA
0
3
where (p; q ) 2 f(1; 1)g and have values according to what region the quadrant occupies of the
(p; q )-plane (Fig. 4, inset). The beam radius, Rp, is dened by the radial size of the beam at the
pupil plane (37.75 mm).
The problem is much simplied if the quadrant masks are oriented such that the edges are
parallel with the x-y axes. This is how our system is operated in practice, deliberately decoupling
the XY tilt motions. In the absence of rotation, Eqn. (4) reduces to
L(p;q) = L0 ? 43Rp (pA + qB);
(5)
{8{
with (p; q ) 2 f(1; 1)g according to quadrant but where the p-q and x-y axes are now aligned.
Equating Eqs. (3) and (5) gives the linear locus of points across a quadrant (p; q ) at which the
plates are separated by exactly L(p;q),
Ax + By = 43Rp (pA + qB):
(6)
Now consider any two quadrants adjacent in the x direction (that is, with common q but opposite
p values). It can be shown by Eqn. (6) that the separation (in x) between the L(p;q)-loci of both
quadrants remains xed at 8Rp=3 for all values of y . In other words, the baseline separating
L(?1;q) and L(+1;q) in the x-direction is a constant, irrespective of y. The same is true for loci
separation in the y -direction along lines of constant x.
Figure 4 shows a side-view along the x-direction of an upper plate (UU 0) tilted relative to
a lower one (x-axis). L(?1;q) and L(+1;q) are the eective plate separations measured in each
quadrant while ZX is the dierence between the two. Without loss of generality we set the
reference quadrant to be on the negative side and the X quadrant on the positive. The oset ZX0
is the amount by which the plate needs correction at the radius of the PZTs and capacitors, Rc .
From Fig. 4 we know through geometrical argument that
c
(7)
ZX0 = 38R
Rp ZX :
We showed in Fig. 3 how an oset such as ZX can be measured directly by the oset of lines
(panels X and ref in the case of the x-oset).
Substituting the radii of the pupil plane beam (Rp = 37:75 mm) and PZTs (Rc = 90 mm)
into Eqn. (7) yields
ZX0 = 2:8ZX :
(8)
This is the relationship we need between measured oset, ZX , and applied (corrective) oset,
ZX0 . It means that any measured oset in the x direction must be corrected by 2:8 times that
oset in the opposite direction. Similar arguments nd an identical scale factor between ZY and
ZY0 . The units in Eqn. (8) can either be the measured software control units or physical units
(m) through Eqn. (1).
The precision of the technique is limited to the smallest steps by which the plates can be
adjusted, not the smallest measurable deviation. By Eqn. (1), the smallest movement is a software
step of 1, equivalent to ZX0 = 0:24 nm or 0:01 % of our smallest plate spacing. This we can
detect through motions as small as 0.09 nm near the plate centre. At the longest wavelengths this
represents =10000. This is much less than the =500 parallelism criterion, over the full range of
TTF wavelengths.
3.3. Phase Reectance at Narrow Gap
{9{
The condition for maximal transmission of light with wavelength through a Fabry-Perot
interferometer is
m = 2L cos ;
(9)
where m is the order of interference, L is the spacing between the plates, is the interior angle
of incidence and is the refractive index of the gap medium. For TTF, this medium is air with
= 1:00. Equation (9) is an approximation suitable for high orders and therefore large plate
spacings. However, it fails to take into account the wavelength-dependent phase-change inherent
in reections between the optical coatings on the inner plate surfaces. Such coatings are optimised
to reect the design wavelength (819 nm for TTF) with zero phase change but incur a lead or lag
phase elsewhere. The phase change becomes increasingly important as the plate spacing becomes
comparable to the thickness of the optical coatings.
Equation (9) can be modied to
(10)
mT + = 2L cos ;
accounting for phase change through the introduction of an order correction term, (Atherton
et al. 1981; Knudtson, Levy & Herr 1996). Here, mT is the true order number associated with
phase correction. The subscript denotes the wavelength dependence of . At large orders mT ,
the eect of the phase change term becomes negligible. The inner coatings of the red TTF cause
to vary by over 630 ? 950 nm.
The ratio mT =m characterises the relative inuence of phase change at a given wavelength.
Combining Eqns. (9) and (10) for a common wavelength and plate spacing L, gives
1
m T
=
1
?
(11)
m L
2 L :
By this we see that the relative size of the phase correction will become larger towards smaller
gap at a given wavelength. In practice, the phase correction will also alter the free spectral range
and bandpass of the instrument, in addition to the shape and location of the transmission prole
(Atherton et al. 1981). Table 1 contains a list of = values at selected wavelengths, as measured
by Queensgate Instruments. Also included are values for the coecient in Eqn. (11).
Figure 5(a) shows four TTF scans at the lowest plate spacings reached by our instrument.
The scans show blended lines of Ne (659.9, 667.8 and 671.7 nm). The lines are unresolved at
all plate spacings except the largest (L = 4:7 m), where they are labelled in (a). The scans
were made at various values of (Zc ; Zs) and transformed to physical units of spacing by Eqn. (2).
Changes in the software scan increment (Zs ) are evident in the dierent sampling densities
of each scan. Observe that the transmission peaks are evenly separated by =2 = 0:33 m,
conrming that the calibration in Eqn. (2) is robust over all settings of Zc and Zs used. Also
note the broadening of the transmitted prole as plate spacing and resolution decreases. The at
background levels are from CCD regions that were not used in the charge shue.
{ 10 {
In Fig. 5(b) we plot the change in mT =m for the same orders of the Ne blend shown in (a).
The ratio mT =m was calculated at each plate spacing measured in (a) by Eqn. (11). Queensgate
Instruments have measured = ?0:79 for TTF at 666 nm. Observe in Fig. 5(b) that phase
correction is a 10 % eect at 670 nm. The dotted lines show the eect to be signicantly
less at wavelengths near the centre of the TTF coverage. The narrowest spacing (2.5 m) is
a self-imposed limit to which we are prepared to drive the plates. Any closer and we run the
risk of damaging the inner coatings by pressing dust particles between the two coating surfaces.
We conclude that at the narrowest spacings of TTF we are in a regime where phase eects are
non-negligible, particularly for wavelengths at the extremities of the optical coating curve.
4. Summary and Future Work
We have resolved a major hurdle to Fabry-Perot tunable lters nding wider use at major
observatories. The pupil Hartmann test described here is fundamental to the application of
tunable lters, particularly at the lowest resolutions (smallest gaps). Our method is sensitive
to deviations as small as =10000 over the optical range. Clearly this technique has far wider
applications in precision measurements of atness.
The Hartmann test achieves plate parallelism across the full 11 m scan range of the TTF.
This has encouraged us to bring the analogue (CS-100) control system under full electronic control.
In the past, switching in hardware to dierent parts of the physical scan range induced small
random oset in the wavelength-gap calibration after returning to a former coarse setting (see
Sect. 2.3). Another benet is `broad-narrow' shuing since frequency switching is now possible
over the full physical range. The slew and settle rates of the capacitance micrometer lead to
overheads of less than 0.01 s. Thus, with charge shuing, two discrete wavelengths can be imaged
side-by-side on the CCD (Bland-Hawthorn & Jones 1998), one set to a narrow bandpass (e.g. 6 A),
the other to a very much wider bandpass (e.g. 40 A).
A limited set of additional renements, currently under development will see the superiority of
tunable lters over monolithic interference lters for an increasing range of imaging applications.
These renements include the development of a `double cavity' TTF which squares the Lorentzian
instrumental prole while maintaining 90% throughput. Graded index coatings and curved plates
will permit such an instrument to be used in fast beams (up to f/2), thereby allowing us to observe
much wider elds than is currently possible.
At present, we isolate single orders of interference with conventional blockers at low resolution
(UBV RIz ), and custom-made intermediate band lters at high resolution. We continue to monitor
developments in acousto-optic and liquid crystal tunable lters (Morris, Hoyt & Treado 1994) for
a suitable `tunable' replacement to our blocking lters. At present, these have insucient clear
aperture (<30 mm), throughput (<30%) and image quality ( 15 m structure) for astronomy at
the cutting edge.
{ 11 {
5. Acknowledgments
We are indebted to John Barton, for his technical expertise, for his excellent AAO-1
CCD controller and his willingness to undertake major developments. We are grateful to
Tony Farrell for the control software, and to Lew Waller, Ed Penny and Chris McCowage for
hardware development. Chris Pietraszewski (Queensgate Instruments) provided us with important
information on the plate coatings. One of us (DHJ) acknowledges the nancial support of a
Commonwealth Australian Postgraduate Research Award.
{ 12 {
REFERENCES
Atherton, P. D., Reay, N. K., Ring, J. and Hicks, T. R. 1981, Opt. Eng. 20(6), 806
Atherton, P. D. and Reay, N. K. 1981, MNRAS 197, 507
Bland-Hawthorn, J. 1995, in 3D Optical Spectroscopic Methods in Astronomy, ASP Conference
Series 71, 369
Bland-Hawthorn, J. and Cecil, G. N. 1996, in Atomic, Molecular and Optical Physics: Atoms and
Molecules 29 B, Chapter 18, eds. F. B. Dunning and R. G. Hulet, Academic Press: San
Francisco, 363
Bland-Hawthorn, J. and Jones, H. 1998, in Optical Astronomical Instrumentation, Proc. SPIE
3355, ed. S. D'Odorico, in press
Clemens, D. P. and Leach, R. W. 1987, Opt. Eng. 26, 9
Cuillandre, J. C., Fort, B., Picat, J. P., Soucail, G., Altieri, B., Beigbeder, F., Dupin, J. P.,
Pourthie, T. and Ratier, G. 1994, Astron. Astrophys. 281, 603
Hicks, T. R., Reay, N. K. and Atherton, P. D. 1984, J. Phys. E. 17, 49
Hicks, T. R. and Atherton, P. D. 1997, The NanoPositioning Book, Queensgate Instruments, Ltd.
Janesick, J. and Elliott, T. 1992, in Astronomical CCD Observing and Reduction Techniques,
ed. S. B. Howell, ASP Conf. Series 23, 1
Jones, R. V. and Richards, J. C. S. 1973, J. Phys. E. 6, 589
Knudtson, J. T., Levy, D. S. and Herr, K. C. 1996, Opt. Eng. 35(8), 2313
Meaburn, J., Anderson, F., Harrington, R. F., Mortleman, J. and Peters, A. 1976, Appl. Opt. 15,
3006
Morris, H. R., Hoyt, C. C. and Treado, P. J. 1994, Appl. Spec. 48:7, 857
Ramsay, J. V. 1962, Appl. Opt. 1, 411
This preprint was prepared with the AAS LATEX macros v3.0.
{ 13 {
(nm)
650
700
750
800
850
900
950
?0:83
?0:69
?0:50
?0:29
+0:32
+0:70
+0:94
2 ?0:23
?0:26
?0:19
?0:12
+0:13
+0:31
+0:45
Table 1: Values of the phase correction term ( ) and related coecient for the red TTF coatings.
Measurements of made by Queensgate Instruments.
{ 14 {
Fig. 1.| Arrangement of components in the optical train for pupil-plane quadrant imaging. Only
the slit and quadrant masks need to be removed to ready the system for astronomical imaging.
{ 15 {
Fig. 2.| Charge-shued long-slit spectrum of a Cu-Ar lamp over 730-788 nm. Shown (from
top to bottom) are lines at 750.90 (doublet), 772.40 (doublet) and 763.51 nm. Wavelength does
not increase sequentially along this frame due to order wrap-around.
{ 16 {
Fig. 3.| Demonstration of how plate tilts are measured and adjusted. Only the central portions
of each full charge shue image are shown and each shue step is an increase of 8 A or =1140.
Panel (a) indicates a small oset in the y -direction only. Panel (b) shows the degraded appearance
of lines at much larger oset. Panel (c) demonstrates the alignment of all lines and attainment of
parallelism. The uneven illumination between panels is due to the poorly diused internal lamp.
{ 17 {
z
q
(-1,+1) (+1,+1)
U’
p
(-1,-1) (+1,-1)
TE
PLA
R
E
P
UP
L0
U
L(-1,q)
∆ZX
L(+1,q)
LOWER PLATE
8
R
3π p
REFERENCE
QUADRANT
∆Z’X
x
Rc
X QUADRANT
Fig. 4.| Side view showing the parameters that quantify plate tilt in the x-direction. Also shown
(inset) is the convention used in labelling quadrants by their (p; q ) 2 f(1; 1)g value.
{ 18 {
1000
500
0
2.5
3
3.5
4
4.5
5
2.5
3
3.5
4
4.5
5
1.2
1.1
1
0.9
Fig. 5.| (a) Four scans of blended Ne lines at the narrowest TTF plate spacings. The lines
are only partially resolved at the largest gap and have been labelled with their wavelengths in
nanometres. (b) Values of mT =m for the orders measured in (a). The rise in this ratio towards
lower gap demonstrates the increasing importance of wavelength-dependent phase change at the
lower limits of TTF operation. The dotted lines show mT =m calculated for wavelengths of 0.8 and
0.85 m.