The ALMA Optical PointingSystems

Design Considerations, PrototypeDescription, and Production Model

Suggestions

Jeff Mangum (NRAO)DRAFT

June 20, 2005

Contents

1 Introduction 1

2 Design Considerations 12.1 Optical Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1.2 Centroid Determination Probability . . . . . . . . . . . . . . . . . . 22.1.3 Resolution and Field-of-View . . . . . . . . . . . . . . . . . . . . . 32.1.4 Mounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 CCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Frame Grabber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Control PC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.5 Star Catalogs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.6 Data Acquisition and Analysis System . . . . . . . . . . . . . . . . . . . . 6

3 Summary Design Requirements 7

4 Prototype Design Characteristics 104.1 OPT Monitor and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2 OPT Image Viewing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.3 OPT Design Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5 Current Limitations 11

A Peak Finding Algorithm 16

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Abstract

This document describes the optical pointing telescope systems for the ALMA prototypeantennas, including detailed descriptions of the telescope specification, design, and control.These optical pointing systems are used to assess the stability and accuracy of the ALMAantenna tracking system and the form and stability of the ALMA telescope pointing be-havior. They served as fundamental tools for the diagnostic tests conducted on the ALMAprototype antennas, and those tests to be conducted on the ALMA production antennas.We also list suggested production model design changes.

1 Introduction

Optical pointing systems have become standard equipment on millimeter and submillimetertelescopes. There are benefits and limitations associated with the reliance on opticalpointing systems on radio telescopes:

1. Benefits:

(a) There are many more bright stars which can be used as optical pointing sourcesthan radio pointing sources.

(b) With a CCD camera, optical data acquisition can be done on time scales asshort as a few tenths of a second, as opposed to the tens of seconds time scalesnecessary for radio pointing measurements.

(c) Positions of optical stars can be derived to sub-arcsecond accuracy, which is amuch higher precision than that obtainable through single antenna radio mea-surements.

2. Limitations:

(a) Differences between the position and behavior of the optical and radio signalpaths can make the derivation of the radio pointing coefficients from opticalpointing measurements difficult.

(b) Optical pointing is not possible during overcast weather conditions.

(c) Optical pointing cannot be used in the daytime, unless the system has beendesigned with near-infrared sensitivity.

Optical pointing systems find application in such areas as:

• Pointing and tracking diagnosis

• Pointing coefficient derivation and monitoring

• Auto-guiding

2 Design Considerations

An optical pointing system for the applications described above can be constructed fromoff-the-shelf commercial components. The main components of the optical pointing systemare:

• Optical telescope

• Commercial CCD camera (with near-infrared sensitivity if daytime observations aredesired)

• PC-based or self-contained frame grabber

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• Control PC

• Data acquisition and analysis system

In the following, we discuss the design considerations for each of these components.

2.1 Optical Telescope

2.1.1 Sensitivity

The optical telescope system should be sensitive enough to detect large numbers of astro-metric stars (which represent a small subset of the existing stars at any given magnitude)with exposures of no more than a few seconds. The magnitude sensitivity of an opticaltelescope and camera system can be derived from the magnitude relation:

ma −mb = 2.512 log10

[(Da

Db

)2]

(1)

where ma and mb are the limiting magnitudes and Da and Db are the diameters of twooptical telescope systems. The optical pointing system that was used on the 12 MeterTelescope had a 3.′′25 (8.255 cm) refracting telescope and Cohu 4810 uncooled CCD cam-era, which resulted in an overall limiting magnitude of about 7. For example, assumingthat mb = 9.5 in Equation 1, if we use the same CCD camera we need an optical telescopewith a diameter 3.1 times as big as the one in 12 Meter Telescope optical pointing system,or Db = 10.′′2 (25.908 cm). Equivalently, magnitude sensitivity can be gained by using amore sensitive CCD camera.

The sensitivity requirements for an optical pointing telescope differ from those for anoptical guiding system. If one can construct a system which is sensitive to a limiting visualmagnitude of about 10, then in any given field it is likely that there will be an astrometricstar which can be used for pointing or tracking. For pointing alone, a limiting visualmagnitude of 7 is sufficient to provide several hundred astrometric stars which can be usedto derive pointing characteristics.

2.1.2 Centroid Determination Probability

The reliability of our determination of the centroid of our point source measurements is oneof the limitations of this optical pointing system. In order to characterize this centroidingsensitivity, we have run a series of simulations which derive the centroid of a point source.The point source is assumed to be located in the center of the image and to have a FWHMof 1 pixel. Synthetic images with random noise and varying peak point source intensitieswere constructed and fit with gaussian models. For each peak signal-to-noise ratio a seriesof 10,000 fits were performed. If a gaussian fit derived the known centroid position inboth axes to within at least n

10pixel, the fit was deemed a success. Since we generally

have a pretty good guess as to where the pointing source in an OPT image should be, thegaussian fit routine in these simulations was given this position as an estimate to the fit.Two values for n were assumed in the simulations: 1 and 3. Figure 1 shows the resultsfrom these fits. From these simulations we find that:

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Figure 1: Gaussian fit simulation results.

• A signal-to-noise ratio of 12 is required to derive the centroid of a gaussian pointsource with 50% confidence for centroid determination to at least 0.1 pixel.

• A signal-to-noise ratio of 7 is required to derive the centroid of a gaussian pointsource with 50% confidence for centroid determination to at least 0.3 pixel.

2.1.3 Resolution and Field-of-View

The detector will be a CCD placed in the focal plane. Atmospheric seeing will limitthe actual resolution to about 1′′–5′′. Since the ability to find the centroid of a star isproportional to the actual resolution divided by the signal-to-noise of the measurement,the pointing precision is much less than the actual resolution. A resolution of about 1′′ perCCD pixel should be sufficient.

The plate scale and diffraction limit of the optical telescope system is given by:

PS = 206.2648×(

1

Mf

)arcsec/µm (2)

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Figure 2: Optics layout with Barlow lens.

θdiffract = 1.22

(λ

D

)radians

= 2.516431× 105

(λ

D

)arcseconds (3)

where f is the focal length of the telescope in millimeters and M is the magnification factorby any additional optics in the system, such as a Barlow lens. Note that the magnificationof a Barlow lens is given by the following:

M =dBarlow

fBarlow

+ 1 (4)

where dBarlow is the distance from the detector (CCD) to the Barlow lens. The opticslayout when a Barlow lens is included is shown in Figure 2.

By combining the plate scale with the length (lCCD, in µm), width (wCCD, in µm), andnumber of samples in the horizontal (Nl) and vertical (Nw) dimensions, we can derive the

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field-of-view (FOV) and effective plate scale (EPS) of the optical pointing system:

FOV = PS × lCCD × wCCD arcsec× arcsec (5)

EPS = PS

(lCCD × wCCD

Nl ×Nw

)arcsec× arcsec (6)

Note that Nl and Nw are the smaller of the number of CCD pixels in each dimension andthe sampling produced by the frame grabber.

2.1.4 Mounting

The mounting of the optical pointing system should meet the following requirements:

• It should be rigidly attached to the structure of the telescope so that it mimics themotion and flexure of the radio telescope structure.

• It should have a remotely-controlled focus translation stage which does not adverselyaffect the optics stability.

• It should be accessible.

Two traditional locations for optical pointing systems are the prime focus and the backupstructure (where an access hole in a panel must be made).

2.2 CCD

The requirements for the CCD detector are driven by the need for sub-arcsecond spatialresolution. Most commercial CCD detectors have a sufficient number of pixels and sensitiv-ity to meet these requirements. For daytime operation, extended near-infrared sensitivityis a feature that can be found on many commercial CCD detectors.

2.3 Frame Grabber

The frame grabber should conform to the type of control computer (in this case, a PCI-busbased PC). It must be able to process at least the same number of pixels as exist in theCCD and have sufficient memory and frame transfer capacity to process images which area few seconds in duration. The dynamic range of the frame grabber should be comparableor greater than that of the CCD camera.

2.4 Control PC

The requirements for the control PC are not very stringent. Any PC with a > 200 MHzprocessor will be sufficient. The operating system used is determined by the requirementsfor the frame grabber driver, data acquisition, and analysis systems.

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2.5 Star Catalogs

Two derivatives of the full Tycho-2 catalog are currently available within the ATF monitorand control system:

TYCHO: The full Tycho-2 catalog.

TYCHO NDS: A filtered version of the Tycho-2 catalog which has been filtered for“double” stars. The algorithm used to eliminate neighbours puts stars into a gridof cells whose size is 10′ × 10′. RA is scaled by cos(Dec) to account for shorteningat Dec = ±90. After the stars have been placed in these cells, then each cell isinspected for neighbours. The distance to all stars in neighboring cells is measured.If the absolute distance is < 10′, the star is deleted from the catalog. Also, if there ismore than one star in the current cell, then all of those other stars are deleted fromthe catalog.

2.6 Data Acquisition and Analysis System

The data acquisition and analysis system for the ALMA optical pointing system operatesas follows. Items displayed in italics are options which might be implemented in the future:

1. The telescope control computer sends commands to the optical pointing computer(OPC) for setup and initialization:

(a) Turn on power to camera.

(b) Open shutter.

(c) Open solar filter.

(d) Select filter position.

2. Using the tycho graphical user interface (GUI) on the antenna control computer, asubset of available stars based on defined selection criteria are selected from a mastercatalog of astrometric stars.

3. For the chosen list of astrometric stars, the control computer and OPC execute thefollowing for each target star:

(a) The telescope control system does some OPT hardware initialization, whichincludes the measurement of a dark frame taken with the OPT shutter closed.

(b) The telescope control computer sends the J2000 source coordinates to the radiotelescope positioning system, and the radio telescope slews to the star. Oncethe star is acquired, frame integration begins.

(c) The telescope control computer calculates the required integration time based onthe magnitude of the target star and commands the OPC to set the integrationtime to this value.

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(d) The frame grabber acquires images of the star at a rate of 8–10 frames per sec-ond. The PC reads the CCD array from the frame grabber buffer and integratesthe signal for a user-specified integration time (0.5 second is a typical value) (orfor the integration time sent down from the control computer).

(e) The integrated image is acquired.

(f) The dark frame is removed from the image.

(g) The centroid of the target star is computed by the control computer as follows:

i. Measure peak pixel location.

ii. Calculate the RMS noise floor near the peak. There are two cases for thiscalculation:

A. If the peak is within the inner half of the CCD frame, calculate theRMS over a 101×101 pixel area around the peak, excluding the 19×19pixel area centered on the peak.

B. If the peak is outside the inner half of the CCD frame, calculate theRMS over a the entire CCD frame, excluding the 19 × 19 pixel areacentered on the peak.

The advantage of doing the RMS calculation in this way is that the cal-culation is not influenced by the non-uniform background produced by theCCD (during daylight observations, mainly).

iii. Measure the exact centroid of the peak using a “center-of-mass” peak de-tection algorithm described in Appendix A

(h) Calculate the signal-to-noise from the peak and RMS calculations done above.

(i) If the signal-to-noise of the measurement meets the signal-to-noise limit set bythe observer, the results of the centroid calculation are written to a file for laterprocessing.

4. Once all of the available stars are measured, analysis of the centroiding results aredone off-line.

5. If we are done using the optical pointing system, the control computer sends someshutdown commands to the OPC, such as:

(a) Turn off power to camera

(b) Close shutter

(c) Close solar filter.

3 Summary Design Requirements

In the following we list some considerations for each component in the OPT design. Asummary of these considerations is given in Table 1.

Primary:

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• The prototype OPTs had a limiting visual magnitude of about 9 for an integra-tion time of a second or two. This indicates that a primary diameter of 4 inchesis sufficient for both the primary (pointing) and secondary (tracking) needs.

• As NAOJ has found that the Meade 102ED lens cell used in the prototypes maybe the source of the measured focus change in these devices, the lens cell glassshould be made of low-expansion coefficient material.

Mount: Low-expansion material is crucial. The rolled Invar used in the prototypes workedvery well. CFRP would be an acceptable (and lower-weight) alternative.

Camera:

• The Cohu 4920 cameras used in the prototypes worked quite well. There noise,pixel size, and dynamic range properties should be followed for the productionmodels.

• One option that is more trouble than it is worth is the extended infrared sen-sitivity. The gain of a few hundred nanometers in spectral response was notworth the effort. IR filtering is enough for daytime measurements.

• If digital camera technology has advanced sufficiently, a digital camera mightbe an attractive option. This could potentially avoid the hassle of having to usea video camera with a frame grabber.

• Nonuniformity in the CCD response was a slight problem for daytime observa-tions (confuses the peak finding algorithm). Would be useful to have a moreuniform CCD response.

Other Optics:

• Barlow Lens. Yes. Improves plate scale without significant loss of sensitivity.

• Focuser. Yes. The design added to the prototypes works quite well and is stable.

Frame Grabber: If necessary. The 8-bit frame grabber used in the prototypes was alimitation. A 16-bit frame grabber would be much better.

Control PC: If necessary (digital camera might provide onboard frame transfer over eth-ernet). Any modern laptop running linux will do.

Control Software: The ATF design worked just fine, and will require only minor improve-ments.

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Table 1: Summary ALMA Optical Telescope Requirements

Telescope D ≥ 4′′ refractor

f/9 (920mm focal length) or longer

Low-expansion material mount (rolled Invar or CFRP)

Low-expansion lens material

Additional Lenses X2 Barlow

Filters IR continuum (λ > 700nm) and clear focus correction

Camera > 56 dB dynamic range

≥ 768× 494 pixels

≥ 8 µm pixel size

Response uniformity

Frame Grabber > 1024× 1024 array capability

> 640× 480 sampling (RS-170)

>2MB VRAM

>4ms frame transfer

> 96 dB (16 bit) dynamic range

Control PC Any modern laptop

Control Software ATF design

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4 Prototype Design Characteristics

4.1 OPT Monitor and Control

Monitor and control of the optical pointing telescope is done by entering commands viaa python interface. In the following, it is assumed that “opt” is defined as the opticaltelescope on antenna number 1 (OPT1):

Monitor Points

Shutter Status: opt.Shutter()

Solar Filter Status: opt.SolarFilter()

Filter Status: opt.IrFilter()

Photodetector Status: opt.PhotoDetector

Telescope Tube Temperature: opt.TubeTemperature

CCD Temperature: opt.CCDTemperature

Electronics Temperature #1: opt.ElectronicsTemp1

Electronics Temperature #2: opt.ElectronicsTemp2

Control Points

Camera Control

Enable Motor Power: opt.enableMotorPower()

Disable Motor Power: opt.disableMotorPower()

Shutter Control

Open Shutter: opt.openShutter()

Close Shutter: opt.closeShutter()

Solar Filter Control

Open Solar Filter: opt.openSolarFilter()

Close Solar Filter: opt.closeSolarFilter()

Filter Control

Open Filter: opt.openIrFilter()

Close Filter: opt.closeIrFilter()

Frame Grabber Commands

Start Exposure: opt.startExposure( exposureTime )

Wait Exposure: opt.waitForExposure()

Abort Exposure: opt.abortExposure()

Write FITS Image: opt.writeFITS( fileName )

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Query Exposure Time: opt.exposureTime

Query Image X Size: opt.sizeX

Query Image Y Size: opt.sizeY

Query Exposure Time Remaining: opt.timeRemaining

4.2 OPT Image Viewing

Image frames can be previewed using a separate application, but to write FITS files ofimages, the command line interface must be used. To run the image viewing application,execute the command optView. The window that pops up has one entry box, two buttons,and an image area. The entry box is used to set the integration time in seconds. Be awarethat the integration time is not calibrated, and there are significant delays in transmittingthe image via CORBA over ethernet, so don’t expect an image right after the time youentered has elapsed. However, the integration time is a multiple of the value entered inthe box, so it is useful to adjust this number. Finally, the image pixel values are scaled toeight bits before being displayed, so the effects of changing the integration time may notbe visually obvious.

Images are “grabbed” with the “grab image” button. One can then follow this with a“writeFITS” command via the python interface.

4.3 OPT Design Summary

1. Figure 3 shows a picture of the OPT1 system.

2. Table 2 lists the design properties for the prototype ALMA optical pointing systems.

3. Table 3 lists the prototype OPT component properties.

4. Figure 4 shows a plot of the spectral sensitivity of the Cohu 4920 CCD camera withextended IR sensitivity (“EXview HAD CCD”).

5. Figure 5 shows a plot of a representative measurement of the OPT1 interior andexterior temperatures, along with the meteorological conditions, for a typical day.

6. Figure 6 defines the axes orientations for OPT1 and OPT2.

5 Current Limitations

Focus Drift: Both OPTs experience a slow focus drift over a period of several hours. Thedrift is about 500 µm in magnitude, and its source is not understood, although testsby NAOJ indicate that the primary lens material may be the source of the problem.Re-focusing with the focus translation stage solves this problem.

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Figure 3: The ALMA OPT1 optical pointing telescope.

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Figure 4: Spectral sensitivity characteristics for ICX248AL CCD in Cohu 4920 camera

Figure 5: Recent measurement of the OPT1 interior and exterior temperatures, along withthe meteorological conditions, for a representative day in October 2003.

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Table 2: Prototype ALMA Optical Telescope Specifications

Telescope Meade 4′′ model 102ED Apochromatic Refractor

f/9 (920mm focal length)

NRAO-design rolled Invar tube and mount

Additional Lenses X2 Barlow

Filters IR continuum (λ > 700nm) and clear focus correction

Camera Cohu 4920-3000 camera

Extended IR sensitivity to 900nm

56 dB dynamic range

768× 494 pixels

8.4× 9.8 µm pixel size

6.4× 4.8 mm image area

Frame Grabber Imaging Technologies PC-Vision

1024× 1024 array capability

640× 480 sampling (RS-170)

2MB VRAM

4ms frame transfer

48 dB dynamic range

Control PC 200 MHz Pentium

Control Software NRAO design

Diffraction Limit 1.′′2 (for λ = 500 nm)

Plate Scale 0.1121 arcsec/µm

Effective Plate Scale 1.′′12× 1.′′12 per detector pixel

Field of view 12′ × 9′

Sensitivity ≥ 7th magnitude in 5 second exposure

Mount location Backup structure (requires access hole in panel)

Mount Three-point Invar; accessible

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Table 3: OPT1 Component Properties

Primary

Model Meade 102ED Apochromatic Refractor

Clear Aperture 4 inches (102 mm)

Focal Length 920mm (f9)

Diameter 110mm

Near Focus 50 feet (15.24m)

Barlow Lens

Model Antares

Magnification 2

Focal Length 42mm

Filters

IR Filter Murnaghan IR-C-Cell-1.25

IR Filter Bandpass 100% transmission @ λ > 700nm

Focus Corrector Murnaghan FC-Cell-1.25

CCD Camera

Model Cohu 4920-3000

Frequency Range (see Figure 4)

Active Pixels 768× 494

Pixel Size 8.4× 9.8 µm

Image Area 6.4× 4.8 mm

Video Output 1.0V p-p, 75Ω, unbalanced

Signal-to-Noise 56 dB @ gamma=1, gain=0 dB

Cooling Normal (5± 2C); Tamb = 5 – 25 C

Hot Ambient (10± 2C); Tamb = 10 – 30 C

Maximum (≥ 22C below ambient), Tamb = 25 – 45 C

Ambient (no cooling); Tamb = –20 – 45 C

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(0,0)OPT1

(0,0)

Y−P

ixel

Elevation

OP

T1

OP

T1

OPT1 Azimuth

X−PixelOPT1

OP

T2

Azim

uth

OP

T2

X−P

ixel

OPT2 Y−Pixel

OPT2 ElevationOPT2

Figure 6: Orientation of the (Az,El) and (X,Y) axes on the ALMA optical pointing tele-scope CCD detectors.

IR Focus Difference: Even though the focal point when the IR filter is inserted shouldbe the same as the focus when the focus corrector is inserted, it isn’t. Re-focusingwith the focus translation stage solves this problem.

Frame Grabber Dynamic Range: The frame grabber dynamic range (48 dB) is lessthan that of the CCD (56 dB). The production OPTs should use a frame grabberwith higher dynamic range (something like 16 bit would be good).

Peak Finding Algorithm: The peak finding algorithm currently suffers from a non-static 1 pixel “quantization” under high intensity (either bright stars or daytime)conditions.

A Peak Finding Algorithm

The following “centre-of-mass” algorithm was suggested by Ralph Snel.

1. Select a sub-image, such as 19× 19 pixels centered on the brightest pixel.

2. Let x = [−3 − 2 − 10123] etc., replicated in the y direction, and y the transpose ofx. Then the center of light of the subimage has coordinates:∑

(x ∗ sub image)∑(sub image)

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∑(y ∗ sub image)∑

(sub image)

3. The biggest practical problem with the OPT is finding out whether or not there isany saturation, in particular during daytime measurements.

Here is a sample bit of C-code to describe this algorithm:

sum_x=0;

sum_y=0;

sum_image=0;

for (j=-lim;j<=lim;j++)

for (i=-lim;i<=lim;i++)

sum_x+=(sub_image[i,j]-avg)*i;

sum_y+=(sub_image[i,j]-avg)*j;

sum_image+=(sub_image[i][j]-avg);

x_centroid=sum_x/sum_image;

y_centroid=sum_y/sum_image;

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