The Field of View of a Thin Lens Interferometer

1
The Field of View of a Thin Lens Interferometer
Pathlengths from in phase positions Top
Channel 2Bsinq(F-Bsinq)/cosf Bottom
Channel (FBsinq)/cosf
2Bsinq
B
2 Channels in Phase here
B
Bsinq
f
F
q
f
Nulled here.
Baseline2B
Frange from array center to detector
2
The Field of View of a Thin Lens Interferometer
Approximations
Pathlengths from in phase positions Top
Channel 2Bsinq(F-Bsinq)/cosf Bottom
Channel (FBsinq)/cosf
APPROXIMATIONS DeflectionAngles of each
Channel ff Cos Approximation cosf
1-f2/2 Taylor Expansion q/(1dx) q(1-dx) Also
Assumed Internal workings of both lenses are
identical!
OPD between top and bottom channels OPD
Bf2sinq
f
F
q
f
Nulled here.
Baseline2B
Frange from array center to detector
3
Q Given the OPD between the channels, what is
the condition to NOT seriously distort a fringe
on the detector?
A OPD lt l/10 Note that this condition also
defines the field of View for an interferometer
of this type.

• OPD between top and bottom channels
• OPD Bf2sinq
• qFOVl/(10f2B)
• lF2/(10B3)

NOTE This FOV calculation makes no assumptions
about maximum graze Angles. Therefore, at most,
the FOV will be 0.5 degrees due to graze
restrictions.
4
Designing a Mission 1Baseline, Focal Length,
FOV, and Formation Tolerances are derived.
What angular resolution at what wavelength do you
want? qres, l
Tightest Formation Flying Tolerance between
optics s/c s. Lateral
What is the smallest X-ray pixel size(mm) you can
imagine? s
The baseline (2B) needs to be 2B l/ qres
The Focal Length (F) needs to be F s/qres
Longitudal Formation Flying Tolerance between
optics s/c 4/5 (s/l)2 qresB
The FOV will be FOV 4/5 (s/l)2 qres
5
Some Typical Numbers 1
6
Designing a Mission 2
What angular resolution at what wavelength do you
want? qres, l
Tightest Formation Flying Tolerance between
optics s/c s. Lateral
What is the smallest X-ray pixel size(mm) you can
imagine? s
The Difference Here is That we will have fringes
10x bigger than the CCD pixel Size.
The baseline (2B) needs to be 2B l/ qres
The Focal Length (F) needs to be F 10 s/qres
Longitudal Formation Flying Tolerance between
optics s/c 80 (s/l)2 qresB
The FOV will be FOV 80 (s/l)2 qres
7
Some Typical Numbers 2
8
Mirror Module Dimensions

• The Mirror modules are pairs of flat (better than
  l/100) mirrors.
• One mirror is fixed, the other has pitch (mas)
  and yaw (arcminute) control.
• The module also has the ability to adjust the
  spacing of the mirrors at the nm level to
  introduce angstrom pathlength control.
• Thermal control consistent to maintain optical
  figure (0.1 degrees).
• There is structure to hold the module together.

9
The Mass of Glass 1
msin(g)
If a mirror length is m, and the graze angle is
g, then the width of the mirror is msin(g)- in
order to have square effective areas for each
module. The effective area of one module will
be Amodule (rmsin(g))2 Where r is the
reflectivity off one mirror.
m
Some Numbers r0.8 g2 degrees sin(g)1/30 gt
Amodule m2/1400
10
The Mass of Glass 2
msin(g)
The 1/6 rule suggests that the thickness of the
mirror be about 1/6th the length in order to
preserve figure. If the density of the mirror is
s, then the mass of the glass of one module
is Mglass sm3sin(g)/3
m
m/6

• Some Numbers
• s2.5 g/cc
• sin(g)1/30
• Mglass m3/16 grams
• (m in cm)

11
The Mass of Glass 3
msin(g)
Some Numbers s2.5 g/cc sin(g)1/30
The ratio of mass to effective area
becomes Mass/area r2ms/(3sin(g))
m
m/6

• NOTE- this mass estimate is for glass only.
  There may be some scaling of masses for structure
  and actuators- but that is not considered here.

12
Actuator Requirements
The pitch control should be to the some fraction
of the diffraction spot size. dql/(msin(g))30l
/m 6 mas for m100 cm, 62 mas for
m10cm 30 nm of control for anysize
mirror. The range of pitch control should be able
to accommodate the range of baselines over the
range of focal lengths. qmax B/F l/(20s)
1 arcsecond of range 5x10-6m of
linear range for a mirror of length m. where
sCCD pixel size
13
What would one of these modules look like?
msin(g)
msin(g)
m
m/3 msin(g)
3/2md
2(wgap)msin(g) By 2(wgap)msin(g)m/3actuator
encoder ASSUME wgap5 cm Encoderencoder5cm S
in(g)1/30 --gt(10cmm/30)x(15cmm/3m/30) --gtm30
cm-gt 13cmx26cm
m/6
Gapmsin(g)
Yaw ontrol
Pitch Control
14
Packing into a Rocket