The Field of View of a Thin Lens Interferometer

Baseline=2B

F

F=range from array center to detector

’

Nulled here.

B

B

2Bsin

Bsin

2 Channels inPhase here

Pathlengths from “in phase” positions:

Top Channel2Bsin+(F-Bsin)/cos’

Bottom Channel(F+Bsin)/cos

The Field of View of a Thin Lens Interferometer: Approximations

Baseline=2B

F

F=range from array center to detector

’

Nulled here.

Pathlengths from “in phase” positions:

Top Channel2Bsin+(F-Bsin)/cos’

Bottom Channel(F+Bsin)/cos

APPROXIMATIONS:

DeflectionAngles of each Channel: ’~Cos Approximation: cos~ 1-2/2Taylor Expansion: q/(1+dx) ~ q(1-dx)Also Assumed: Internal workings of

both lenses are identical!

OPD between top and bottom channels:

OPD ~B2sin

OPD between top and bottom channels:

OPD ~B2sin

FOV=2B) = F2/(10B3)

Q: Given the OPD between the channels, what is the condition to NOT seriously distort a fringe on the detector?

A: OPD < Note that this condition also defines the field of View for an interferometer of this type.

NOTE: This FOV calculation makes no assumptions about maximum grazeAngles. Therefore, at most, the FOV will be ~0.5 degrees due to graze restrictions.

Designing a Mission 1:Baseline, Focal Length, FOV, and Formation Tolerances are derived.

What angular resolution at what wavelength do you want? res

What is the smallest X-ray pixel size(m) you can imagine? s

The baseline (2B) needs to be:2B = res

The Focal Length (F) needs to be:F = s/res

The FOV will be:FOV = 4/5(s/)2 res

Tightest Formation Flying Tolerance between optics s/c = s.“Lateral”

Longitudal Formation Flying Tolerance between optics s/c =4/5(s/)2 resB

Some Typical Numbers 1 “MAXIM Pathfinder”

100 as Science

(5x10-10 radians)

Angstroms

S=10m

F=20 km2B= 2 mFOV=2.5 arcsecondsLong. Control=0.7 mm

“Full MAXIM”

1 as Science

(5x10-12 radians)

Angstroms

S=10m

F=2000 km2B= 200 mFOV=25 masLong. Control=7 m

Designing a Mission 2:

What angular resolution at what wavelength do you want? res

What is the smallest X-ray pixel size(m) you can imagine? s

The baseline (2B) needs to be:2B = res

The Focal Length (F) needs to be:F = s/res

The FOV will be:FOV = 80(s/)2 res

Tightest Formation Flying Tolerance between optics s/c = s.“Lateral”

Longitudal Formation Flying Tolerance between optics s/c =80(s/)2 resB

The Difference Here isThat we will have fringes 10x bigger than the CCD pixelSize.

Some Typical Numbers 2 “MAXIM Pathfinder”

100 as Science

(5x10-10 radians)

Angstroms

S=10m

F=200 km2B= 2 mFOV=250 arcsecondsLong. Control=7 cm

“Full MAXIM”

1 as Science

(5x10-12 radians)

Angstroms

S=10m

F=20000 km2B= 200 mFOV=2.5 arcsecondsLong. Control=700 m

Mirror Module Dimensions•The Mirror modules are pairs of flat (better than /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.

The Mass of Glass 1:

If a mirror length is “m”, and the graze angle is “g”, then the width of the mirror is m*sin(g)- in order to have square effective areas for each module.

The effective area of one module will be:

Amodule= (r*m*sin(g))2

Where r is the reflectivity off one mirror.

m

msin(g)

Some Numbers:

r~0.8

g~2 degrees

sin(g)~1/30

=> Amodule~ m2/1400

The Mass of Glass 2:

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 , then the mass of the glass of one module is:

Mglass= m3sin(g)/3

m

msin(g)

Some Numbers:

~2.5 g/cc

sin(g)~1/30

Mglass~ m3/16 grams

(m in cm)

m/6

The Mass of Glass 3:

The ratio of mass to effective area becomes:

Mass/area = r2m/(3sin(g)) m

msin(g)

Some Numbers:

~2.5 g/cc

sin(g)~1/30

m/6

Mirror Length (cm)

Area/Module

(cm2)

Glass Mass Per Module

(kg)

Number of Modules to get 1000 cm2 area.

Total mass of glass to get 1000 cm2

(kg)

10 0.071 0.0625 14000 875

30 0.643 1.688 1555 2624

100 7.143 62.5 140 8750

•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.

Actuator Requirements:The pitch control should be to the some fraction of the diffraction spot size.

(m*sin(g))~30/m

~ 6 mas for m=100 cm, 62 mas for m=10cm

~ 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.

max~ B/F = s)

~ 1 arcsecond of range

~ 5x10-6m of linear range for a mirror of length m.

where s=CCD pixel size

What would one of these modules look like?

m

msin(g)

m/6

Gap~msin(g)

Yaw ontrol

Pitch Control

msin(g)

3/2m

+d

m/3

+ m

sin(

g)

2(w+gap)+msin(g)By2(w+gap)+msin(g)+m/3+actuator+encoder

ASSUME: w+gap~5 cmEncoder+encoder~5cmSin(g)~1/30

-->(10cm+m/30)x(15cm+m/3+m/30)-->m=30cm-> 13cmx26cm

Packing into a Rocket