LGS wavefront sensor : Type and number of sub-apertures

1. LGS wavefront sensor : Type and number of sub-apertures NGAO Team Meeting #4 V. Velur Caltech Optical Observatories 01/22/2007

2. Presentation Outline • Introduction - WBS dictionary definition • LGS WFS type – • Assumptions • Handling extended LGS spots • Pulse tracking techniques and comparison • Number of sub-apertures - procedure • Narrow field case SHWFS • Narrow field case PWFS • Wide field case SHWFS • Wide field case PWFS • Bad seeing, cirrus conditions on SHWFS and PWFS • Conclusions

3. WBS dictionary definition • 3.1.2.2.6: Consider alternative WFS designs (e.g. Shack-Hartmann vs. pyramid) for different laser pulse formats. Evaluate and compare the advantages of e.g. short pulse tracking using radial geometry CCDs and mechanical pulse trackers. Complete when LGS WFS requirements have been documented. • 3.1.2.2.7: Consider the cost/benefit of supporting different format LGS wavefront sensors (e.g. 44 subaps across, vs. 32, vs 24.) Consider the operational scenarios required to meet science requirements in poor atmospheric seeing or cirrus conditions?

4. LGS WFS type • For this study I have only considered a Shack Hartmann and a Pyramid WFSs. • Assumptions:

5. Handling an extended LGS spot • The baseline design of NGAO uses a 150W from CW laser(s). The LGS spots from these will produce elongated spots on the WFS even if projected from the center. • spot elongation (in seconds) is given by: 206264.81 (sec/rad)* (s * t * (cos(z))^2)/(h^2); • Minimum spot size at the farthest sub-aperture when projected from the center (in the radial direction): (5 * 10 * 10^(3) * 1)/((90*10^3)^2)*206264.81 = 1.28 arcsec

6. How a Shack Hartmann WFS handles elongated spots: • Use sub-apertures that have a FoV greater than spot size in the radial direction. This can be done by binning or by choosing a suitable plate scale. But comes at the cost of extra noise in the sensor • Use radial geometry CCDs as LGS WFS - Beletic et. al. are funded by AODP and CARA to develop low noise CCD detectors with a planar JFET based amplifier on a back-thined device (CCID-56b). The noise estimates from these rectilinear CCDs is very encouraging (1 e− RON at 1 MHz pixel rate). The radial versions of these devices, as shown in figures 1 2, will be well suited to handle a CW laser spots that are centrally projected. To reduce centroiding error due to elongated spots either a noise optimal centroiding algorithm or a matched filter scheme can be used. • Use a mechanical resonator to keep the spot in focus (will talk about it in detail later in the presentation).

7. How a pyramid WFS handles elongated spots • Learn to work with an elongated spot. The only reference (Igelesias et. al.) that I could find suggests that this is feasible. The paper deals with performing WF sensing on the human eye and claims that a point pyramid WFS becomes twice as sensitive (at the cost of linearity) when working with an extended object. So, in principle one could build a sensor that has the capture range (linearity) and appropriate sensitivity. Word of caution : There is no SNR calculations and the fact that there is no similar paper from the astronomical community this approach must be further investigated, if not ignored! • Use a mechanical pulse tracker or some other pulse tracking scheme (see descriptions later). This will give the PWFS the advantage of working with a AO corrected spot rather than a blurred spot due to elongation (or a sub-aperture limited spot size as seen by the SHWFS). The effect of this in terms of wavefront error is shown in the second part of the presentation.

8. Pulse tracking schemes for 1-3 microsec lasers: • Radial geometry CCDs (only good for a SHWFS):

9. Mechanical pulse tracker • Built out of 6Al14V Titanium alloy or some similar aluminum alloy. • The geometry of the resonator may be step, exponential or a hybrid horn with active cooling. • The input transducer stresses the input end and this is manifested as motion on the other end. The design makes sure that the output end remains flat when the motion is induced. • We may have to give the resonator manufacturer the mirror specification (size, weight, density, geometry etc.), and we may have to figure out a bonding technique that will withstand ultrasonic operation. • For example, a 20 KHz resonator is 5” in length and 3” at the transducer end and 0.25” at the output. The size for a 50 KHz resonator is approximately 2/5 th. The lower the natural frequency the greater the amplitude obtained from the resonator. Typical amplitudes obtained from a 20 KHz resonator is 300 microns. So a 50 KHz resonator will yield a stroke of ~120 microns. • Georges et. al. describe a optical system that can convert a 15 mm focus shift (native to telescope/AO) to a 120 micron motion. The design uses 14 extra optical surfaces. We may come up with a more novel design. • The cost of the resonator is between $2500 - $3500 (word-of-mouth quote from Krell Engineering depending on complexity). There are multiple vendors for drive electronics (Branson Ultrasonics, Sonics and Materials etc.) and the cost for the electronics is about $4000. These units consume about 2KW of power.

10. Georges et. al.’s optical design

11. Other schemes (B. Bauman’s ideas) • Use of 2 orthogonal cylindrical lenses with a continuously varying RoC shaped to fit along the circumference of a rotating disc. Uses only 4 extra surfaces! • Mechanical MEMS resonator Comparison table:

12. Number of Sub-apertures Trade Study • In this trade study merit is indicated by WFE (based on Rich’s error budget tool) and the laser power required is assumed to be cost driver (without actual mention of $ value). It also assumes that the complexity in switching plate scales and lenslets in not the cost driver! • The study looks at the performance of the NGAO system with SHWFS and PWFS using 44, 32 and 24 sub-apertures all working with a 64 actuator DM in wide field and narrow field conditions. • Narrow field case : on axis TT star w/ 10% of TT path light going to a slow WFS, TT star mv = 19, Chris Neyman's atmospheric parameters, SCAO, quincunx radius=5 arcsec. The H - band Strehl was optimized by varying the TT and HOWFS loop rate. • Wide field case: sky coverage = 15% (19 mv star limit with a search radius that is varied). I optimize HO integration time, TT int. time, TT guide star brightness (at the cost of search radius) to optimize H band Strehl. The LGS asterism radius is set to 33 arc-sec. as suggested by KAON429.

13. Narrow field case SHWFS

14. Narrow field PWFS

15. Wide field SHWFS

16. Wide field PWFS

17. PWFS vs. SHWFS • When modeling a PWFS the spot size advantage during centroiding is used, also the charge diffusion is set to zero (which is assumed to be .30 pixels based on Palomar #s, this is different from van Dam’s #s). • Will present plots and tables on the report.

18. Bad seeing conditions • No cirrus and r0=0.10 m, wind velocity = 15.0 m/s, laser power = 150W • Bad seeing and bad laser (which I also assume is bad cirrus condition, which is optimistic because I don’t account for the extra scatter caused by the extinction) - r0 = 0.10 m, wind velocity = 15.0 m/s and laser power = 50W. The extra scatter will be accounted for after the results from the Rayleigh scatter study are in.

19. Bad seeing, Cirrus clouds cases:

20. Conclusions • If we are going to be using a CW laser it is easiest to work with a SHWFS and a radial geometry CCD. Both technologies are mature (as compared to counterparts) and the advantage of PWFS is only a few nm in WFE as presented by current models. • With a pulsed laser, still the option of SHWFS with a radial format CCD, seems like the simplest and most efficient way to proceed w.r.t pulse trackers. • It is useful to have the option of multiple sub-apertures only in case of low laser power at the 50W level. Otherwise there is only a few nm of WFE difference between the 32 sub-apertures and 44 sub-aperture case. The 24 sub-aperture case performs quite badly except for the 50W laser power case. So the EC must make a choice of either 24 and 32 sub-apertures or 24 and 44 sub-apertures if the incremental cost or packaging constraint of supporting 3 lenslet gets to be too much work. • In case of bad seeing, serious Cirrus conditions only narrow field science must be performed and 32 sub-aperture case gives optimal performance for both cases. There is no significant difference between the PWFS and SHWFS case. For the wide field case the WFE in case of bad seeing and cirrus is 610 nm and that in case of bad seeing and no cirrus is 567nm.