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Report M001

Pupil Plane Combiner Slab and Spacers Requirements
Julien Coyne
jc466@mrao.cam.ac.uk Revision 3.1 - Tuesday, Novemb er 21th, 2006

Astrophysics Group Cavendish Lab oratory University of Cambridge Cambridge CB3 0HE United Kingdom


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Contents
1 Intro duction 1.1 Measuring visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Visibility requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Slabs and spacers 2.1 Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Spacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 P4S 3.1 3.2 3.3 3.4 3.5 3.6 combiner Geometry . . . . . . . . . . . Parameters . . . . . . . . . . Blo cks . . . . . . . . . . . . . (2,1,2) layout . . . . . . . . . Coatings comp ensation . . . . Tolerancing . . . . . . . . . . 3.6.1 Slabs . . . . . . . . . . 3.6.2 Spacers . . . . . . . . 3.6.3 Coatings comp ensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 4 6 6 6 8 8 8 9 10 10 11 11 11 12

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Preface
The COAST research group (Cambridge Optical Ap erture Synthesis Telescop e) from the Cavendish Lab oratory, University of Cambridge, is working on the design of a new b eam combiner for an astronomical interferometer. The concept is a 4 way-in, 4way-out combiner. The basic layout of the combiner is describ ed. The aim of this do cument is to present the slabs and spacers requirements for this b eam combiner layout.

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Chapter 1

Introduction
1.1 Measuring visibilities

An astronomical interferometer combines the light from several telescop es on a single instrument. One way of combining the collimated light b eams (diameter : 18 mm in our case) coming from different telescop es is to use b eam splitters. As in a table-top Michelson interferometer, the intensities of the output b eams are a function of the optical path differences b etween the b eams. In an astronomical interferometer, an optical path delay (OPD) is added to each b eam b efore reaching the b eam combiner. When the OPDs are time-mo dulated, temp oral fringes are measured at the outputs. By carefully cho osing the path mo dulation frequencies, it is then p ossible to retrieve the fringe pattern for each pair of b eams and compute the fringe contrasts (also called visibilities ). Since the sp ectral band considered is quite large (up to ab out 50 nm, b etween 1.1 µm and 2.4 µm), the fringe packet is extremely small in the OPD space. The visibility measurements can then b e used to reconstruct an image of the star the telescop es are p ointing at.

1.2

Visibility requirement

The visibility requirements are simply that the maximum allowable visibility loss inside the combiner due to the slabs and spacers geometry is 5%, and that the geometrical comp ensation of the coatings (see section 3.5) should not intro duce more than 0.5% visibility loss. This directly translates into a set of sp ecifications for the slabs and spacers : any nonnominal thickness, angle or p osition will intro duce a b eam tilt, a b eam shear and/or an optical path difference that will degrade one or several visibility measurement(s). Three typ es of errors on the slab shap e have b een identified : see Fig. 1.1. The requirements for the spacers derive from the sp ecifications of several Fabry Perot etalons as explained in the following chapters. Likewise, three typ es of errors on an etalon shap e have b een identified : see Fig. 1.2. A home grown ray tracing co de has b een used to compute the slabs and etalons requirements.

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Figure 1.1: The 3 typ es of errors on the slab shap e : thickness (dd), angle around Oz b etween the useful surfaces (d1 ) and angle around Oy b etween the useful surfaces (d 2 ). The b eams are travelling in the Oxy plane.

Figure 1.2: The 3 typ es of errors on an etalon shap e : thickness (dd), angle around Oz b etween the useful surfaces (d1 ) and angle around Oy b etween the useful surfaces (d 2 ). The b eams are travelling in the Oxy plane.

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Chapter 2

Slabs and spacers
2.1 Slabs

The length and thickness requirements for the slabs are presented in the next chapters.

Figure 2.1: Slabs : geometry. The grey area represent the part of the surface that must b e of optical quality. The minimum height of the slabs is set by the size of the b eams (see Fig. 2.1). The optical b eams have a diameter of 18 mm. They all travel in the same plane. Therefore the working part of the slabs of optical quality must b e at least 20 mm wide. Spacers separate the slabs. Slabs and spacers are optically contacted. The height of the slabs should allow for the additional surface required to have the slabs and spacers optically contacted, while preserving the 20 mm strip of optical quality through which the b eams will travel. The two surfaces of the slabs the optical b eams are travelling through must have a surface flatness of lamb da/20 p eak-valley (at 633nm) and have a cosmetic quality (scratch-dig) of 40-20. The other surfaces do not need to b e to b e p olished. The b ottom surface must b e p erp endicular to the left and right surfaces (the two surfaces through which the b eams travel) to b etter than 1 degree. The slabs must b e highly transparent over a large sp ectral bandwidth (from 1.1 µm to 2.4 µm) hence the choice for the glass : Infrasil 301.

2.2

Spacers

The optical layout envisaged consists of two slabs and two mirrors separated with (and optically contacted to) glass spacers. The pupil plane combiners layout can b e considered as several stacked Fabry Perot etalons. The requirements for the spacers derive directly from the requirements on the Fabry Perot 6


etalons. The optical b eams should not travel through the spacers. The role of the spacers is purely to set the distances b etween the surfaces of the etalons and to maintain them parallel. The geometry of the spacers is left to the discretion of the glass manufacturer. To comply with the thermal stability requirements of the combiners, the glass chosen for the spacers is : Zero dur Expansion Class 2.

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Chapter 3

P4S combiner
3.1 Geometry

The layout of the P4S combiner is presented on Fig. 3.1 (top view). It is comp osed of 2 slabs and 2 mirrors. Four input b eams (1, 2, 3 and 4 on Fig. 3.1) are combined and app ear at each of the four output b eams (I, I I, I I I and IV on Fig. 3.1).

Figure 3.1: P4S b eam combiner.

3.2

Parameters

The incidence angle of the b eams is equal to = 15 o . The layout has 3 free parameters : · d1 : the distance b etween b eams 1 and 2, · b : see Fig. 3.1, · ds : thickness of the slabs. 8


The other parameters can b e computed from the formulae : a=b+ c= d1 2sin( ) (3.1) (3.2)
1

d1 sin( )

d2 = 2bsin( ) + d d3 = d
1

(3.3) (3.4)

3.3

Blo cks

It is p ossible to design a layout such that the thicknesses of the spacers are all multiples of the same smaller thickness (see Fig. 3.2) : · La = Lb + Lc /2 = k d · Lb = l d
X X X X

· Lc = md

with k , l and m integers, and d

a real numb er.

Figure 3.2: P4S Combiner - spacers. From a practical p oint of view, this allows to use small identical blocks (thickness of the blo cks : dX ) to build the spacers : spacer Sa is made of k optically contacted blo cks, spacer S b of l blo cks and spacer Sc of m blo cks. With this typ e of layout, the thickness d X of the blo cks and the thickness ds of the slabs are the free parameters. There are no requirements on the absolute thicknesses of the blo cks or the slabs (only on the difference b etween the thicknesses of the blo cks/slabs).

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3.4

(2,1,2) layout

Such a layout with a reasonable slab thickness, based on the triplet (k , l, m) = (2, 1, 2) and with the minimal blo ck thickness dX has the parameters (see Fig. 3.3) : · a = 194 mm · b = 107 mm · c = 174 mm · ds = 20 mm · d1 = 45 mm · d2 = 100 mm · d3 = 45 mm ·d
X

= 87 mm

Hence the length of the spacers : · La = 174 mm · Lb = 87 mm · Lc = 174 mm
300 250 200 150 100 50 0 -50 -100 -150 -200 -100

0

100

200

300

400

500

Figure 3.3: Ray tracing : (2,1,2) Layout. Minimal size. All units are in mm.

3.5

Coatings comp ensation

The equation presented in the previous sections do not take into account the coatings on the slabs and on the mirrors. To comp ensate for the additional path lengths intro duced by the coatings, the spacers Sb and Sc (see Fig. 3.2) must b e slightly smaller than the computed value from these equations. The exact thicknesses X b and Xc that must b e shaved of the spacers Sb and Sc will dep end on the coatings design (order of magnitude : a few microns) : the lengths of the spacers Sb and Sc should actually b e (L b - Xb ) and (Lc - Xc ). 10


3.6
3.6.1

Tolerancing
Slabs

Both slabs have the same dimensions : · Length : 230 mm ± 0.5 mm · Height : see chapter 2 · Thickness : ds - in range 10mm - 30mm The vendor may cho ose any value of ds in the range 10 mm - 30 mm to minimise the overall cost needed to meet the other requirements. All things b eing equal, smaller values of d s are desirable. See table 3.1 for the glass slabs requirements. dd ­ 0.6 µm d1 1.2 arcsec 0.4 arcsec d2 1.3 arcsec 0.4 arcsec

max diff

Table 3.1: Slabs requirements. max : maximum allowable error. diff : maximum allowable difference b etween slabs.

3.6.2

Spacers

Spacers separate the comp onents.

Figure 3.4: P4S b eam combiner layout : 3 Fabry Perot etalons separated by glass slabs. For the purp ose of detailing the requirements, the layout can b e considered as 3 stacked Fabry Perot etalons separated with glass slabs (see Fig. 3.4) : · Etalon A : b etween surface 1 and 2 · Etalon B : b etween surface 3 and 4 · Etalon C : b etween surface 5 and 6

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The optical layout presented in section 3.4 allows the use of small identical building blo cks for each spacer : 2 blo cks for spacer Sa (Etalon A), 1 blo ck for spacer Sb (Etalon B) and 2 blo cks for spacer Sc (Etalon C). The requirements for the blo cks are presented on table 3.2. dd ­ 0.9 µm d1 0.3 arcsec 0.4 arcsec d2 0.3 arcsec 0.4 arcsec

max diff

Table 3.2: Blo cks requirements. max : maximum allowable error. diff : maximum allowable difference b etween blo cks. The vendor may cho ose any value of dX in the range 85 mm - 150 mm to minimise the overall cost needed to meet the other requirements. All things b eing equal, smaller values of d X are desirable. As already stated in chapter 2, the geometry of the spacers is left to the discretion of the glass manufacturer.

3.6.3

Coatings comp ensation

A few microns will have to b e shaved of spacers Sb and Sc (see section 3.5). The exact values X b and Xc will dep end on the coatings designs. The requirements on the accuracy for this reduction of the length of Sb and Sc is : 0.3 µm

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