# Presentation: 108868

## Optical Phasing SensorsYoung-Hartmann SensorYoung-Shack-Hartmann Sensor

- Chanda Bartlett Walker
- Dr. H. Philip Stahl
- Dr. Michael Lloyd-Hart
- May 2001

## Outline

- _[Introduction](slide3.xml)_
- _[Phasing concepts](slide5.xml)_
- Phasing Camera System
- Dispersed Fringe Sensor
- _[New phasing concepts](slide12.xml)_
- Young-Hartmann Sensor
- Simulations and theory
- Questions and Discussion
- Young-Shack-Hartmann Sensor
- Simulations
- _[Conclusions](slide43.xml)_

## Introduction: Motivation

- Larger aperture telescopes are required to enable remote sensing and astronomy to continue to expand scientific knowledge.
- Segmented telescopes allow lighter and smaller packages for space travel.
- Segmented telescopes must be aligned in (at least) three axes--tip, tilt and piston.

## Introduction: Motivation

- Point Spread Function
- Generated by a 6 segment mirror
- Random piston positions                 
- OPD  <  4	                       OPD  <  /4

## Phasing Concepts

- MECHANICAL METHODS
- Edge sensors – Hobby-Eberly, PAMELA
- OPTICAL METHODS
- Phase Diversity – JPL, LPARL, Ball, DCATT, etc.
- Phase Diverse Phase Retrieval – Keck, DCATT, LPARL, etc.
- Phase Discontinuity Sensing – Keck
- Far-Field Optimization – LPARL
- Phasing Camera System – Keck
- Dispersed Fringe Sensor – Palomar, DCATT, AOA
- Young-Hartmann Sensor – PAMELA
- Young-Shack-Hartmann Sensor – PAMELA

## Phasing Concepts: Phasing Camera System

**Phasing Camera System***
**Uses sub-apertures at the edges of each segment pair**
**The interference pattern indicates the piston misalignment**
**Uses multiple measurement techniques to achieve absolute alignment**
**Narrowband measurement**
**Broadband measurement**
**Capture Range: 30********m**
**Alignment capability: 0.1 ********m**

- sub-apertures

- *G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, “Phasing the mirror segmetns of the Keck telescopes:
- the broadband phasing algorithm,” Appl. Opt. 37, 140-155 (1998).

## Narrow-band Measurement

Fringe pattern moves with OPD
Since this method has a 2 ambiguity, it is implemented after the OPD is less than 1 .

**Fringe pattern moves with OPD**
**Since this method has a 2******** ambiguity, it is implemented after the OPD is less than 1 ********.**

**Phasing Concepts: ****Phasing Camera System**

**Broadband Measurement**
**Fringe pattern loses contrast with OPD**
**This pattern has a large capture range and can achieve sub-wavelength alignment.**

- OPD 
******/2     ********/4           0      -********/4    -********/2**

- OPD 
** ****40********     10********     < ********    -10********   -40******

## Phasing Concepts: Phasing Camera System

- ADVANTAGES
- Simple/fast mathematics
- Large capture range
- Sub-wavelength alignment capability

- DISADVANTAGES
- Critical mask alignment
- Samples of the edge of the segments
- Samples only a small portion of the segment
- Steals irradiance from science camera

## Phasing Concepts:Dispersed Fringe Sensor

**Dispersed Fringe Sensor***
**Uses grisms aligned with the edges of each segment pair**
**The wavelength dispersed interference pattern indicates the piston misalignment**
**Uses a broadband source to achieve absolute alignment**
**Capture Range: system dependent ~10’s ******
**Alignment capability: ******** ******** ********/50**

- *Wirth, A., “Cophasing Methods for Segmented Mirrors,” Adative Optics Association
- Basinger, S. A.; Redding, D. C.; Lowman, A. E.; Burns, L.A.; Liu, K.Y.; Cohen, D., “Performance of wavefront sensing and
- control algorithms on a segmented telescope testbed,” SPIE Proc. **4013**, 749-756 (2000).

## Fringe pattern shifts per wavelength

**Phasing Concepts: ****Dispersed Fringe Sensor**

**Each segment pair yields a pattern such as this**
**The period of the pattern determines the OPD**

****

****

## Phasing Concepts: Phasing Camera System

- ADVANTAGES
- Simple/fast mathematics
- Large capture range
- Sub-wavelength alignment capability if the image is sampled sufficiently

- DISADVANTAGES
- Samples of the edge of the segments
- Samples only a small portion of the segment
- Segment aberrations can substantially change interference pattern
- ?Mask alignment critical?
- Steals irradiance from science camera

## Phasing Concepts:Young-Hartmann Sensor

**Young-Hartmann Sensor**
**Uses sub-apertures centered to each segment**
**A change in the interference pattern versus wavelength indicates the piston misalignment**
**Uses multiple wavelength measurements to achieve absolute alignment**
**3 Narrow-band measurement**
**Broadband measurement**
**Capture Range: system dependent 10-100’s ******
**Alignment capability: sub-wavelength with a calibration image**

## Phasing Concepts:Young-Hartmann Sensor

**Phasing Concepts:****Young-Hartmann Sensor**

**Based upon a Hartmann array  **
**The aperture plate is placed in the pupil plane**
**Followed by a diffractive optic**
**The central beam (0th order) could be used to indicate slope error for tip/tilt alignment but is presently filtered out.**
**First order beams from adjacent segments overlap to create an interference pattern for relative phase measurements**

## Young-Hartmann Sensor:

**Three apertures with grating structure superimposed**

**Young-Hartmann Sensor:**
**Simulations and Theory**

**Image of pupil plane with showing the 0****th**** and ±1****st**** orders**

## Young-Hartmann Sensor:

**Young-Hartmann Sensor:**
**Simulations and Theory**

**Image of the pupil plane without filtering the 0****th**** order.**

**Image of the pupil plane with filtering of the 0****th**** order.**

## Young-Hartmann Sensor:

**Young-Hartmann Sensor:**
**Simulations and Theory**

- Magnified interference pattern with the two mirrors co-phased
- The central fringe lies under the green bar

- Magnified interference pattern with the two mirrors 180° out of phase
- The fringe pattern has shifted relative to the green bar

## Young-Hartmann Sensor:Simulations and Theory

**Two interference patterns are captured per segment pair**
- Each pattern is created with a monochromatic source with a different wavelength
**From each interference pattern, a phase map is calculated**
- I(x,y) = 1 + COS( 2 **** OPD(x,y) **/******) = 1 + COS(****)
- Since a linear tilt is the dominant structure,  is easily gathered without the need for phase shifting techniques.

- Simulated
- Irradiance Maps

**                                           ********1                                   ********2**

## Young-Hartmann Sensor:Simulations and Theory

****(x,y) = 2 **** OPD(x,y) **/ ******
****e(x,y)  = ****1(x,y) - ****2(x,y)
- = 2 **** OPD(x,y) **((**1**/******1)-(1**/******2**))**** **
**=**** **2 ****** **OPD(x,y)** ****/ ******e

**                             ********1                                       ********2**

- Simulated
- Phase Maps

**For example:**
****1 = 600nm
****2 = 633nm
****e = 11.5m

## The OPD can be calculated by subtracting the two piston maps pixel-by-pixel.
e(x,y)  = 2  OPD(x,y) / e
OPD(x,y) = e(x,y) *e / 2  

****e(x,y)  = 2 ****** **OPD(x,y)** ****/ ******e
- OPD(x,y) = ****e(x,y) *****e **/ **2 ****** **

**Young-Hartmann Sensor:****Simulations and Theory**

- Simulated
- equivalent phase
- Mirror segments
- are co-phased

- Simulated
- equivalent phase
- Mirror segments
- are offset by
- < 1
- Pattern has shifted relative to the co-phased simulation

- To return to questions and discussion click _[here](slide26.xml)_

## A few thoughts on a broadband measurement . . .
These plots are the irradiance distribution created by a broadband source 
 = 500nm – 633nm

**These plots are the irradiance distribution created by a broadband source **
****** ****= 500nm – 633nm**

**Young-Hartmann Sensor:****Simulations and Theory**

**OPD = 0                                  OPD = 1.5 ******** **

## Phasing Concepts: Young-Hartmann Sensor

**Step 1 – Course tip/tilt align mirrors using another sensor**
- This step POSSIBLY could be achieved using this sensor IF:
- The 0th order is not removed
- The imaged plane is not conjugate to the pupil plane
- Fine tip/tilt alignment could be maintained using fringe orientation
**Step 2 – Course phase align**		OPD <45******m ******** 4.5 ********m**
- Use two monochromatic measurements
- Example: 1 = 670nm  2 = 675nm  e = 90.5m
**Step 3 – Fine phase align**		OPD <5.3******m ******** .53 ********m**
- Use two monochromatic measurements
- Example: 1 = 635nm  2 = 675nm  e = 10.7m
**Step 4 – Co-phase mirrors**		OPD < ****** ******** ********/3******** ********/20**
- Use a broadband or monochromatic source with a calibration image
- OR Use phase diversity techniques

## Phasing Concepts: Young-Hartmann Sensor

- ADVANTAGES
- Simple/fast mathematics
- Large capture range
- Samples a large portion segments
- Samples the center portion of the segments

- DISADVANTAGES
- Sub-wavelength alignment capability if there is a calibration image to compare to results.
- Steals irradiance from science camera

## Young-Hartmann Sensor:Questions and Discussion

- Questions to be answered from modeling . . .
- Is my technique of converting irradiance maps to phase maps sufficient? What technique is standard in the interferometry industry? How do I implement the more efficient techniques?
- Is a 3 sample/fringe sample rate sufficient?
- What does theory predict regarding the alignment accuracy of this technique?
- What are the effects of  misalignment of the spots (due to dispersion of the diffractive optic) on the measurement?
- What are the effects of misalignment of the diffractive patterns (due to source misalignment) on the measurement?
- What are the effects of aberrations on the measurement?
- Some of these questions are investigated in the next slides.  The rest are still in progress.

## Young-Hartmann Sensor:Questions and Discussion

- Is my technique of converting irradiance maps to phase maps sufficient? What technique is standard in the interferometry industry? How do I implement the more standard techniques?
- My technique for phase conversion
- Step 1:  Locate the local maxima.
- Step 2:  Determine the number of pixels between adjacent local maxima along a row.
- Step 3:  Assume a linear phase between the maxima and assign the phase according to the number of pixels between the maxima.

## Young-Hartmann Sensor:Questions and Discussions

- Raw Data: Two images generated by GLAD software
- Wavelengths 670 nm and 675nm
-  e = 90.5m
- Piston offset 3.26 waves =  2070 nm

## Young-Hartmann Sensor:Questions and Discussion

- After conversion to phase maps, the subtraction of the two data sets results in the phase map shown on the left
- A cross-section of the phase map through the central horizontal line is shown on the right
- This phase map DOES NOT show the expected tilt from the simulations above . . .why??  (To see expected result click _[here](slide19.xml)__.)_

## Young-Hartmann Sensor:Questions and Discussion

- An average the entire field yields a piston offset of 400.2 nm; the difference between this result and the actual offset is less than 2% of the equivalent wavelength.
- This suggests that /20 alignment capability is feasible.  More simulations with larger OPD are in progress to further validate this capability.

## Young-Hartmann Sensor:Questions and Discussion

- Two images generated by GLAD software.
- Wavelengths 635 nm and 675nm
-  e = 10.7m
- Piston offset 3.26 waves =  2070 nm
- Notice the shifted spots (due to dispersion of the diffractive optic) in the first image.

## Young-Hartmann Sensor:Questions and Discussion

- After conversion to phase maps, the subtraction of the two new data sets results in the phase map shown on the left
- A cross-section of the phase map through the central horizontal line is shown on the top right on the top
- An average along the columns is shown on the bottom right

## Young-Hartmann Sensor:Questions and Discussions

- The tilt still seems to be missing.  Are there hints of other aberrations coming in?
- An average the entire field yields a piston offset of 2314.9nm; the difference between this result and the actual offset is 2% of the equivalent wavelength.

## Young-Hartmann Sensor:Questions and Discussions

- Is my technique of converting irradiance maps to phase maps sufficient?
- With errors of ~2% for both equivalent wavelengths, it seems that it may be sufficient.
- The lack of the anticipated tilt in the simulation is concerning.
- What technique is standard in the interferometry industry?
- Standard technique: Spatial carrier frequency technique
- Step 1:Generate two sets of data
- Set one is the product of the irradiance map with a cosine map at the carrier frequency
- Set two is the product of the irradiance map with a sine map also at the carrier frequency
- Step 2:  The arctan of the ratio of the two new maps yields the phase maps.
- Requires the dc irradiance to be uniform over the pixels required to calculate the phase for one fringe.
- Requires the carrier frequency to be known.

## Young-Hartmann Sensor:Questions and Discussion

- How do I implement the standard technique?
- It is not clear if my data will have a sufficiently uniform dc irradiance over three pixels.
- The carrier frequency would have to be measured.  Perhaps is could be measured once per wavelength after the optical design is fixed.  At worst, it would need to be measured at the beginning of a test.

## Young-Hartmann Sensor:Questions and Discussion

- Is a 3 sample/fringe sample rate sufficient?
- In order to determine the answer to this question, the raw data was interpolated and re-sampled at ~3 samples per fringe.  This matches the sampling rate seen in the lab.

## Young-Hartmann Sensor:Questions and Discussion

- The raw data generated from GLAD had a 9 sample/fringe sample rate.  The measurements in the lab have a 3 sample/fringe rate.
- The plots below compare the results generated with the different sampling rate.  The scales for the plots are the same.
- The plot on the left shows the results from the raw data (9 sample/fringe).
- The plot on the right is shows the results from the lab sample rate (3 sample/fringe).
- Note:  the raw data was interpolated and re-sampled as opposed to throwing out 2 pixels per 3.

## Young-Hartmann Sensor:Questions and Discussion

- The OPD from the average of all pixels was:
- e = 90.5m
- RAW DATA		400.2 nm; 1.8 % error
- LAB DATA		203.2 nm; 2.0 % error
- e = 10.7m
- RAW DATA		2330.1 nm; 2.4 % error
- LAB DATA		2314.9 nm; 2.3 % error
- These results suggest that the phase conversion technique is still sufficient with only 3 samples per fringe.

## Young-Hartmann Sensor:Questions and Discussion

- What does theory predict as the alignment accuracy of this technique?
- Early simulations suggest that e/40 is possible.
-  e/20 is sufficient to capture 50m and reduce the piston offset to sub-wavelength.
- More simulations with larger piston offsets are in progress.

## Phasing Concepts:Young-Shack-Hartmann Sensor

**Young-Shack-Hartmann Sensor**
**Uses sub-apertures centered to each segment**
**The interference pattern indicates the piston misalignment**
**Uses multiple wavelength measurements to achieve absolute alignment**
**3 Narrow-band measurement**
**Broadband measurement**
**Capture Range: system dependent 10-100’s ******
**Alignment capability: sub-wavelength**

## Phasing Concepts:Young-Shack-Hartmann Sensor

**Based upon a Shack-Hartmann lens array  **
**The lens array is placed in the pupil plane**
**One lenslet per mirror segment**
**Followed by a diffractive optic**
**The central beam (0th order) is used to measure slope error for tip/tilt alignment**
**First order beams from adjacent segments overlap to create an interference pattern for relative phase measurements**

## Young-Shack-Hartmann Sensor:Simulations

**Young-Shack-Hartmann Sensor:****Simulations**

- _Apertures of the S-H lenslet array_
- • Lenslet array is placed in the pupil plane.
- • Only the inner ring of segments is represented here.
- • Figures 1 and 2 share the same scale.  Figure 3 has a different scale.

- _Focal plane of S-H_
- _ __lenslet array_
- •  Six spots are generated by the six lenslets in the array

- _Hexagonal segments_
- • Aperture created by the segments of the primary.
- • Only the inner ring of segments is represented here.
- • Aperture is as seen in the pupil plane.

- Figure 1                                               Figure 2                                               Figure 3

## Young-Shack-Hartmann Sensor:Simulations

**Young-Shack-Hartmann Sensor:****Simulations**

- Possible interference patterns resulting if the beams from lenslets 1and 2 overlap and the beams from 4 and 5 overlap.
- •  The interference pattern resulting from beams 4 and 5 are in phase.
- •  The interference pattern resulting from beams 1 and 2 are 180 out of phase.

- 1&2

- 4&5

- Simulated spots and interference patterns at the focal plane of the array with diffractive optic.
- • Spots 1, 2, 4, and 5 are less bright because half of their irradiance has been diverted to form the interference pattern.
- • Only a few spots and diffraction patterns are shown for simplicity.

- 1

- 2

- 6

- 5

- 4

- 3

- Simulated focal plane without diffraction optic.
- There are six focused spots generated by the S-H array.
- Only the inner ring of spots are represented here.

## Phasing Concepts: Young-Shack-Hartmann Sensor

**Step 1 – Tip/tilt align mirrors using 0****th**** order image**
**Step 2 – Course phase align**		OPD <45******m ******** 4.5 ********m**
- Use two monochromatic measurements
- Example: 1 = 670nm  2 = 675nm  e = 90.5m
**Step 3 – Fine phase align**		OPD <5.3******m ******** .53 ********m**
- Use two monochromatic measurements
- Example: 1 = 635nm  2 = 675nm  e = 10.7m
**Step 4 – Co-phase mirrors**		OPD < ****** ******** ********/5******** ********/20**
- Use a broadband or monochromatic source and search for largest irradiance.

## Phasing Concepts: Young-Shack-Hartmann Sensor

- ADVANTAGES
- Simple/fast mathematics
- Large capture range
- Samples a large portion of the segments
- Samples the center portion of the segments
- Sub-wavelength alignment capability
- Achieve tip, tilt and piston alignment with one device

- DISADVANTAGES
- Steals irradiance from science camera
- ?Effects of aberrations not known yet?

## Conclusions

- Comparison between 4 similar optical phasing sensors has been discussed.
- All have the disadvantage of stealing light from the science camera.
- The Young-Hartmann and Young-Shack-Hartmann sensors have the advantage of sampling a large central portion of the segments.
- Capture ranges and alignment capabilities are sufficient for each technique but a calibration image is required for the Young-Hartmann.