By-Eye Active Optics

JMH: What follows below is what we wrote for LBC by-eye active optics. The important change for IRTC at Bent Gregorian F/15 is that there is the tertiary mirror in the beam, so all the pupils have a mirror reflection. At rotator angle zero, this means that the signs of Z5 and Z8 are reversed while Z4, Z6, Z7 and Z11 are unchanged since they have left-right symmetry. (The text and diagrams below have not yet been editted to reflect these changes.)

Wavefront and Collimation Correction

When an extra-focal pupil image has zero aberration it appears perfectly uniform (looks just like the entrance pupil of the telescope). Aberrations in LBC and/or the Primary Mirror cause distortions in the shape and intensity of the pupil image. We can use these distortions to measure and improve the focus, collimation and shape of the primary mirror. We use the size of the pupil (at a given extra-focal offset) to indicate the departure from the ideal focus. We use the centration of the central obstruction to indicate the miscollimation coma. Severe coma alters the light distribution across the pupil and causes the pupil to look like a crescent moon. Ellipticity of the pupil is used to indicate astigmatism which can be corrected by bending the mirror. The relative size of the central obstruction is used to indicate spherical aberration. Especially the measurement of spherical aberration is strongly affected by seeing.

Estimating the Corrections Needed

The extra-focal pupil image taken for focus and collimation is usually close enough to the zero aberration image that the IDL analysis program, lbcfpia, can compute a reasonable set of Zernike coefficients: defocus (Z4); astigmatism (Z5 and Z6); coma (Z7 and Z8) and spherical (Z11) which can be sent to the primary mirror to correct its shape (to the PSF subsystem of the telescope control system). If the diameter of the pupil image is way too small or large, lbcfpia will compute and send only Z4. A second extra-focal image will then have a diameter close enough to the nominal one that the other corrections can also be computed. Usually 1 or 2 iterations are all that are needed to converge to a good focus and collimation; if the numbers output by lbcfpia are within errors (of order 100-300 nanometers), send these and go on to the science observation.

But sometimes, especially at the start of the night and when there has been a large change in temperature, the extra-focal pupil image is far from the zero aberration one and lbcfpia cannot analyze it; some manual intervention is needed. The observer will have to identify the aberration and estimate the magnitude and sense of the correction needed. The following equations and diagrams are intended to help with this. Give the Zernike coefficients to the operator, who will enter them in the PSF subsytem. Ensure that the other coefficients are set to 0 in the PSF GUI when changing only one coefficient say Z7 manually.

Focus

The nominal diameter of a pupil image taken with the primary mirror -0.80 mm below focus is 60.256 pixels.

If the extra-focal pupil images you obtain are much larger or smaller than 60 pixels and lbcfpia does not output any value for Z4, then you should estimate the value of Z4 needed and ask the operator to input this. A quick way to measure the diameter of the extra-focal pupil image is to use the 'ruler' in ds9. Load the image in ds9, click the button 'Region' and then 'ruler' (or 'more...' first to get the set of buttons which includes 'ruler'). Then position the mouse cursor over one point along the edge of the extra-focal pupil, click and hold the left button and drag the cursor along the diameter to the point on the other edge, 180 degrees away. The length of the ruler in pixels is displayed.

To estimate the value of Z4 which the operator should apply [in nanometers], multiply the difference between the measured diameter and 60.256 pxl (60.256 - meas diameter) by the ratio, -184.4 nm/pxl. Note that applying a positive Z4 will decrease the diameter of the extra-focal pupil. This ratio, delta_Z4 / delta_pxl = -184.4 nm/pxl, is a combination of the two empirically determined relations between diameter [pixels] and Z position of primary [mm]:

• abs(delta_pxl/delta_focus) = 75.32 pxl/mm (every 0.013mm move in Z away from focus causes a 1pixel increase in the pupil diameter)

and Z position of primary [mm] and Z4 [nm]:

• delta_Z4/delta_focus = 1000/0.072 nm/mm (note that the units for Z4 are nanometers and for Z they are millimeters).

JMH: The above equation seems to be wrong: Empirically, PSF moves M1 37.9 microns when you ask for 1000 nm rms wavefront Z4 as LBC on 20210401. ARakich says 37.7 microns from Zemax.

Note that since the other Zernike coefficients are computed from the deviations of the extra-focal pupil image (its shape, the diameters of its inner and outer edges) from the un-aberrated pupil image obtained for the primary mirror -0.8mm below focus, the above pixel-to-nanometer scaling factor also applies to these, albeit in a less direct way.

Coma, Astigmatism and Spherical

This set of cartoons should help the observer to identify whether there is coma, astigmatism or spherical and indicate which Zernike coefficient needs to be applied and the sense of the correction. The magnitude may be gauged from the -184.4 nm/pxl scaling factor, but usually the corrections are applied first in increments of 500 or 1000 nm, which produce a noticeable effect; finer tuning can be handled by lbcfpia which should work once the extra-focal pupil image is close to the nominal diameter and fairly evenly illuminated.

Orientation of Extra-Focal Pupil Images

The spider arm can be seen on the extra-focal pupil image. In good seeing it appears sharp and detailed while in poor seeing it may appear only as a dark triangle with apex pointing to the pupil center. The opening angle of this triangle(spider) changes with instrument rotator angle. Knowing the instrument rotator angle (not position angle!) is crucial to determining the sense of the aberration and which Zernike coefficient (Z5 or Z6; Z7 or Z8) needs to be changed to collimate the telescope. Use these relations with the "By-Eye AO" crib sheet to determine the coefficient that needs to be applied.

• Rotator Angle = 0 deg <---> Spider opens downward (to -y) on image (reverses on an intra-focal pupil)
• Increasing Rotator Angle <---> image (field & pupil) rotate counter-clockwise
• Decreasing Rotator Angle <---> image (field & pupil) rotate clockwise

Relationship between Zernike coefficients and Mirror Position displayed on the PSF Collimation Form.

The PSF Collimation Form (normally only the telescope operator will have it displayed) shows the 6 coordinates which describe the position of the primary mirror: translation (X,Y,Z) in millimeters and tilt (RX,RY,RZ) in arcseconds. The values along the top row are the sums of the contributions from the following sources:

• the collimation lookup table (function of elevation and temperature, determined last fall)
• active optics corrections sent from the instrument (these will be updated each time that results of lbcfpia are sent)
• instrument focus offset (these will be updated upon changing filters, according to the LBC filter focus offsets)
• global offsets (usually all zeros)

When an extra-focal pupil image is analyzed and the Zernike coefficients sent, these arrive at the PSF subsystem of the telescope control system (TCS). The TCS determines how to process these. Defocus (Z4) and coma (Z7 and Z8) change the mirror position and will be seen as changes in the values of X,Y,Z in the 'active optics' and top rows of the PSF Collimation Form. Note that coma is corrected (in our adopted strategy) by translating the primary mirror, not by tilting it also. +Z7 commands a +Y move of M1 and +Z8 commands a +X move of M1. Astigmatism (Z5 and Z6) and spherical (Z11) apply bending forces to the mirror and will not show up in the PSF Collimation Form.

Coma-free repointing of the primary mirror for binocular co-pointing and for slave guiding

To change the pointing of LBC for either adjusting the binocular co-pointing or for slave-mode guiding, we translate and rotate the primary mirror in such a way as to introduce no coma. This means rotating the primary mirror about a point 9808 mm in front of the primary (a bit above the prime focus). The following numbers are based on Zemax calculations by A. Rakich and E. Diolaiti plus empirical observations (to get the signs right) by J. Hill on 24-Nov-2007.

Prior to May 2008:

1.00 arcsec of EL motion requires +0.0485 mm Y displacement of the primary plus +1.02 arcsec of RX tilt. These are implemented through PSF as +136 nm Z7 plus -20750 nm Z3. This causes the star images in the LBC focal plane to move up (+Y on chip 2) at rotator angle 0 degrees, and to move down (-Y on chip 2) at rotator angle 180 degrees.

1.00 arcsec of AZ motion requires +0.0485 mm X displacement of the primary plus -1.02 arcsec RY tilt. These are implemented through PSF as +136 nm Z8 plus -20750 nm Z2. This causes the star images in the LBC focal plane to move left (-X on chip 2) at rotator angle 0 degrees, and to move right (+X on chip 2) at rotator angle 180 degrees.

After May 2008:

1.00 arcsec of EL motion requires +0.0485 mm Y displacement of the primary plus +1.02 arcsec of RX tilt. These are implemented through PSF as +56.82 nm Z7 plus -157.4 nm Z3. This causes the star images in the LBC focal plane to move up (+Y on chip 2) at rotator angle 0 degrees, and to move down (-Y on chip 2) at rotator angle 180 degrees.

1.00 arcsec of AZ motion requires +0.0485 mm X displacement of the primary plus -1.02 arcsec RY tilt. These are implemented through PSF as +56.82 nm Z8 plus -157.4 nm Z2. This causes the star images in the LBC focal plane to move left (-X on chip 2) at rotator angle 0 degrees, and to move right (+X on chip 2) at rotator angle 180 degrees.

Coma correction by PSF

Prior to May 2008:

+1000 nm of Z7 correction causes PSF to displace the mirror by +0.357 mm in Y.

+1000 nm of Z8 correction causes PSF to displace the mirror by +0.357 mm in X.

After May 2008:

A tip-free coma adjustment would require rotating the primary mirror about a point 19200 mm in front of the primary, the vertex center of curvature.

+1000 nm of Z7 correction causes PSF to displace the mirror by +0.8536 mm in Y plus +9.17 arcsec RX.

+1000 nm of Z8 correction causes PSF to displace the mirror by +0.8536 mm in X plus -9.17 arcsec RY.

Tip-Tilt correction by PSF (creates coma)

Prior to May 2008:

+1000 nm of Z2 causes PSF to tilt the mirror by +0.0491 arcsec RY.

+1000 nm of Z3 causes PSF to tilt the mirror by -0.0491 arcsec RX.

After May 2008:

+1000 nm of Z2 causes PSF to tilt the mirror by +0.0491 arcsec RY.

+1000 nm of Z3 causes PSF to tilt the mirror by -0.0491 arcsec RX.

-- Main.okuhn - 19 Dec 2006; -- JohnHill - 28 Jan 2008