MAXIM

Webster CashUniversity of Colorado

Sne

SNR

Log

Dia

met

er (

cm)

Log Distance (pc)0 1 2 6543 987 10

6

8

10

12

14

16

18

Maxim

PathfinderHSTChandra

NS Disks

XRB Disks

Stellar Coronae

AGNJets

AGN BLR

AGNEvent

Horizons

GRBAfterglow

InteractingBinaries

CV

XRBOrbits

20

22Star

Clusters

GalaxiesClusters ofGalaxies

Capella 0.0001”

Capella 0.000001”

AR LacSimulation @ 100as

AGN Accretion DiskSimulations @ 0.1as

Courtesy of Phil Armitage, U. Colorado and C. Reynolds, U. Maryland

Need Resolution and Signal

If we are going to do this, we need to support two basic capabilities:

• Signal

• Resolution

X-ray Sources Are Super Bright

Example: Mass Transfer Binary1037ergs/s from 109cm object

That is ~10,000L from 10-4A = 108 B

where B is the solar brightness in ergs/cm2/s/steradian

Brightness is a conserved quantity and is the measure of visibility for a resolved object

Note: Optically thin x-ray sources can have very low brightness and are inappropriate

targets for interferometry. Same is true in all parts of spectrum!

Artist’s impression of Cyg X-1 (NASA)

My Impression

Status of X-ray Optics

• Modest Resolution– 0.5 arcsec telescopes

– 0.5 micron microscopes

• Severe Scatter Problem– Mid-Frequency Ripple

• Extreme Cost– Millions of Dollars Each

– Years to Fabricate

sin1B

2cos12 BB

sin2

sin

2cos121

BBOPD

sin20

cossin20

Baselined

2sin20

focald

Pathlength Tolerance Analysis at Grazing Incidence

A1 A2

S1S2

A1 & A2 in Phase Here

C

If OPD to be < /10 then

A Simple X-ray Interferometer

Flats

Detector

Wavefront Interference

d/L

=s (where s is fringe spacing)

d

Ls

s

Optics

Each Mirror Was AdjustableFrom Outside Vacuum

System was covered by thermal shroud

X-ray Fringes

1.25keVCash et al March 1999

0.5keVGendreau, October 2002

Flats Held in PhaseSample Many Frequencies

As More Flats Are UsedPattern Approaches Image

2 4 8

16 3212

Parallel to Source Direction

To focus

Periscope Configuration

Reduces Sensitivity to BaselineEach Periscope in the array is held to sin

Keeps beam pointedin constant directionlike thin lens

focus

Periscopes allow for delay in eachchannel. Can sample full UV plane.

Periscope Requirements

• Even Number of Reflections

With odd number ofreflections, beam direction shiftswith mirror tilt

With even number, the mirrorscompensate and beam travels in samedirection.

Phase Shift

Path Delay = h sin

h

so h < /10 for phase stability

if h~1cm then < 10-8 (2 milli-arcsec)

This can be done, but it’s not easy.

Phase Delay

)cot(cot2coscot)22sec(sincotsin22seccos(cos 2111122121 dP

d1

d2

)cot(cot2coscot)22sec(sincotsin22seccos(cos 43333424234222 d

There are Solutions

This solution can be direction and phase invariant

Dennis Gallagher has verified this by raytrace!

Pointing can wander arcseconds, even arcminutes, and beamholds fixed!

Array Pointing

• 4 mirror periscopes solve problem of mirror stability

• But what about array pointing?

• Doesn’t the array have to be stable to 1as if we are to image to 1as?

Thin Lens Behavior

As a thin lens wobbles, the image in space does not movePosition on the detector changes only because the detector moves

Formation Flying

If detector is on a separate craft, then a wobble in the lens has no effect on the image.

But motion of detector relative to Line of Sight (red) does!

Much easier than stabilizing array.Still the toughest nut for full Maxim.Variety of solutions under development.

Mirror FEMMirror Face Mirror Back

3pt Ti Flexure Mount

Optic w/FaceSheet Removed

Mirror Analysis SummaryAnalysis Goal/Req. Result Comments

1oc Bulk Temp Load min surface deformation PtoV=6.2nm, RMS=1.2nm

1oc X Gradient min surface deformation PtoV=3.2nm, RMS=0.6nm Gradient across mirror surface

1oc Y Gradient min surface deformation PtoV=3.1nm, RMS=0.6nm Gradient across mirror surface

1oc Z Gradient min surface deformation PtoV=17.0nm, RMS=3.8nm Gradient through mirror thicknessFixed Base Dynamics FF > 100 Hz FF=278 Hz Mirror on flexures, but not entire mount20g Quasi Static Load Mount Stress < Yield 35 MPa maximum 20g Y Loading20g Quasi Static Load Low Mirror Stress 7.6MPa maximum 20g Y Loading

1cZ Mirror Deformations (mm) 20gY Mirror Back Stresses (MPa) Mirror First Mode = 278 Hz

MAXIM Position Tolerances =1nm, F=20,000km, D=1km, m=30cm, =1deg, h=1m

DOF Mirror Equation Periscope Equation

MirrorTolerance

PeriscopeTolerance

X ±1.7nm ±4m

Y ±0.3mm ± 0.5mm

Z ±94.7nm ±0.32m

X-rot(yaw)

±6.9arcmin

± 7.8arcmin

Y-rot(pitch)

±2.3marcsec

± 10arcsec

Z-rot(roll)

±0.13arcsec

±18.5arcsec2D5

F2

)cos()sin(320

D5

F

10

)sin( m

310

)sin( m

)(sin320

)2cos(2

2

2

D5

F4

35

)sin( 15

)sin(

h20

22

10

sin

sin103

1

F

m

m

22

10

sin

sin10sin3

1

F

m

m

Optical Bench FEM

Flexure Fixed Mount

Simplified Optics Mounts

Main Bench

“Daughter” Benches

Periscope Assembly

Entrance Aperture(Thermal Collimator)

Shutter Mechanism(one for each aperture)

Assy. Kinematic Mounts (3)

Launch Configuration LayoutDelta IV ø5m x L14.3m 24 Free Flyer Satellites (4 Apertures ea.)1 Hub Satellite (12 Apertures)1 Detector Satellite

Ø4.75m

Aperture Locations (central area)

26

12

3

45

6

7

8

9

10

11

12

13

14

15

16

17

18

On the left is the probability distribution function for two sources in the same field of view. The central source has an energy half that of the source that is displaced to the lower left. The image on the right shows 9000 total events for this system with the lower energy source having twice the intensity of the higher energy source. Even though the higher energy source is in the first maxima of the other, the two can still be easily distinguished.

Stars

Simulation with Interferometer

Sun with SOHO

Black hole imager

black hole census

black hole physics

space interferometry

The Beyond Einstein Program

LIGO

Chandra

Swift

MAP

Hubble

Science and Technology Precursors

Dark EnergyProbe

optical imaging

Constellation-X

x-ray imaging

LISA

gravitational wave detectors

InflationProbemicrowave background detection

Black HoleSurveyProbehard x-ray detectors

Big BangObserver

dark matter physics

space interferometry, gravitational wave detection

dark energy physics

Bottom Line

• Maxim can be built in an affordable way

• Achieving 0.1mas can be done with modest control in free-flying

• Full black hole imaging for under $900M

• Maxim is in the planning

• NRA for “Vision Mission Studies” coming out this week.