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Image Quality and Stability Criteria ­ Transmissive Systems

Alex Rea adr34@cam.ac.uk

Cavendish Lab oratory, University of Cambridge

FTT Technical Meeting Friday 21st May 2010

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

1 / 19


Table Expansion

If everything is fixed to the table, and the table expands uniformly, then everything moves radially away from the centre of expansion. The absolute change in position of any object depends on the centre of expansion chosen. However, the relative motion of any two objects remains radial, which can be seen by taking the centre of expansion as under one of the objects of interest. So what happens when the light beam is not fixed to the table?

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

2 / 19


Table Expansion and Pupil Shear
I somewhat regret ringing this bell. It should not be a problem after all. Let's look at the geometry.



z

z = 2 в S tan в sin




= z cos = 2 в S в sin2

S

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

3 / 19


Table Expansion and Pupil Shear
Now consider the effect of this displacement on the OAP.
f



f'


f

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

4 / 19


Table Expansion and Pupil Shear
So what effect does this have on the CCD? The image has moved by Observed Shift D в f = T в S в sin2 = T f
D
Shifted Ray Original Ray



Original Focal Plane
Alex Rea (Cavendish Labs, Cambridge) Transmissive Systems

New position of CCD
21st May 2010 5 / 19


Table Expansion and Pupil Shear

So how big a shift does this correspond to? Observed Shift = T в 2 в S в sin2 = 18 в 10-6 K = 15 ; T
max -1

sin 15

1 4

= 5K

Observed Shift 1.125 в 10-5 в S

So this is not going to be a problem after all. Sorry!

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

6 / 19


Transmissive Layouts

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

7 / 19


Transmissive Layouts

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

8 / 19


Image Quality
Criterion was that the spot size should be on the order of the pixel scale across a field of view with side of 20 arcseconds. This field of view is the off-axis field of view we are required to guide within. For the common elements: Degree of Freedom Allowed movement x , y 0.3 z Insensitive x, y Unconstrained z Unconstrained Lens x , y 0.7 z 200µm x, y Unconstrained z Unconstrained The CCD has the same defocus tolerance as the lens, and all other directions are insensitive or unconstrained.
Alex Rea (Cavendish Labs, Cambridge) Transmissive Systems 21st May 2010 9 / 19

Element Dichroic


Image Quality

For the setup with one folding mirror:

Element FM1

Degree of Freedom x , y z x, y z

Allowed movement 0.8 100µm Unconstrained Unconstrained

These figures are reassuringly large.

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

10 / 19


Image Quality
For the setup with two folding mirrors: Element FM1 Degree of Freedom x , y z x, y z x y z x, y z Allowed movement 0.3 Insensitive Unconstrained Unconstrained 0.7 1 200µm Unconstrained Unconstrained

FM2

So again, not too bad. Like the OAP system, it's the stability that is forcing our hand.
Alex Rea (Cavendish Labs, Cambridge) Transmissive Systems 21st May 2010 11 / 19


Image Stability
Criterion was image should not move by more than 0.015 arcseconds, or = 1.63µm for the focal length being considered here. Common elements: Element Dichroic Degree of Freedom x , y z x, y, z x, y x , y z z x, y x , y z z
Transmissive Systems

Lens

CCD

Allowed movement 0.10 arcsec Insensitive Unconstrained 1.63µm 30 arcsec Unconstrained Unconstrained 1.63µm Insensitive Unconstrained Unconstrained
21st May 2010 12 / 19

Alex Rea (Cavendish Labs, Cambridge)


Image Stability

With one folding mirror:

Element FM1

Degree of Freedom z x , y x, y z

Allowed movement 6µm 0.18 arcseconds Unconstrained Unconstrained

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

13 / 19


Image Stability
With two folding mirrors: Element FM1 Degree of Freedom x , y z x, y z z x , y x, y z Allowed movement 0.10 arcseconds Insensitive Unconstrained Unconstrained 1.3µm 0.17 arcseconds Unconstrained Unconstrained

FM2

These are certainly more ominous figures than for the image quality criterion.
Alex Rea (Cavendish Labs, Cambridge) Transmissive Systems 21st May 2010 14 / 19


OAP Mirror vs Lens Comparisons
Dichroic in both cases must be stable to better than about 0.1 arcseconds. This comes from 0.015 в 14 = 0.105 arcseconds 2 The most stringent positional requirement in either system comes from holding the relative shear of the OAP/lens and the CCD to around 1µm. High incident angle folding mirrors must also be held to this accuracy if placed after the lens. There is at least one extra element to hold to high accuracy using the lens and folding mirror arrangement. Is the OAP harder to hold accurately than the lens due to the inherent asymmetry?
Alex Rea (Cavendish Labs, Cambridge) Transmissive Systems 21st May 2010 15 / 19


Sample Error Budget - OAP
What are the stability requirements on each individual component? Element Dichroic Degree of Freedom x , y z x, y x, y z x , y z x, y z x , y z Allowed movement 0.11 arcsecond Insensitive Unconstrained 1.2-2µm 100µm 0.11 arcsecond 0.76 arcsecond 1.2-2µm 100µm Insensitive Unconstrained Limiting Requirement Position of image n/a n/a Position of image Quality of image Position of image Position of image Position of image Quality of image n/a n/a
21st May 2010 16 / 19

OAP

CCD

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems


Sample Error Budget - OAP
Can divide up our sources of error quite nicely: Some constraints affect quality, some position. These can be readily divorced, as where one element affects both, the position requirement is far more stringent. The only two quality requirements are OAP and CCD z , so we can assign 70µm here to each, so the RMS despace is still only 100µm. The constraints that affect position are either angles or shears. Both seem hard, so assign budget equally between the two - each contribute of movement, where is the movement on the CCD equivalent to 2 0.015 arcseconds on the sky. With each of angles and shears, the contribution to x and y movement of the image can be separated (to first order), so each of these can contribute . 2
Alex Rea (Cavendish Labs, Cambridge) Transmissive Systems 21st May 2010 17 / 19


Sample Error Budget - OAP
We have argued our way down to a list of pairs of (approximately) independent and linear variables that each must contribute . So when 2 added in quadrature, we expect each member of the pair to contribute 22 . As they are linear, we can simply take the tolerances found earlier and divide by 2 2. Criterion Quality of Image Position of Image Type of Degrees of Freedom Position Tilt Shear Degrees of Freedom zOAP xD , yD , xOAP , yOAP , , zCCD xOAP yOAP , zOAP xCCD yCCD
21st May 2010 18 / 19

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems


Sample Error Budget - OAP

Doing this, we arrive at a (somewhat naОve) error budget: Element Dichroic OAP Degree of Freedom x , y x, y z x , y z x, y z Allowed movement 0.039 arcsecond 0.43-0.71µm 70µm 0.038 arcsecond 0.17 arcsecond 0.43-0.71µm 70µm Limiting Requirement Position of image Position of image Quality of image Position of image Position of image Position of image Quality of image

CCD

Alex Rea (Cavendish Labs, Cambridge)

Transmissive Systems

21st May 2010

19 / 19