Abstract
In the first chapter we gave a brief review of the RA/Dec coordinate system, and how it is used to write software for observation planning. Here we re-visit the RA/Dec coordinate system in the context of pointing a telescope to a given sky location as specifient: precise knowledge of the current time.
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Notes
- 1.
Why was England so lucky as to be the zero-point for all time on our planet? Good question. Better question: Which landmarks on each of the worlds astronomers are currently exploring will be chosen to be the prime meridian? If you are interested consider reading the report of the IAU/WGCCRE (see reference [1]).
- 2.
Recall, again, that a star is transiting, or “transiting the local meridian” stated in the long form, when it is no longer rising, but has not yet started setting. That infinitesimal instant also is the point at which the star is as close as it’s going to get to being overhead and therefore as close as it’s going to get, in angular terms, to your telescope.
- 3.
Ever wonder what that ‘M’ stands for in AM and PM? Ante Meridian and Post Meridian. At 1:00 PM the HA of the sun is +1 solar hour.
- 4.
As of this writing, C is the obvious choice for this level of software, i.e., the low level pointing and tracking server. See Chapter “Choice of Languages.”
- 5.
In RA/Dec; see “Target Planning” section in “Observation Planning Software” chapter for a review of RA/Dec coordinates; and the “Time” subsection above for our discussion of hour angle (HA).
- 6.
Revisit the first chapter’s section on target planning to review the use of arcminutes to measure distance if this reference to arcminutes as a distance is confusing.
- 7.
OSIRIS at WMKO for example.
- 8.
Recall that the terms altitude and elevation are synonymous in this context and used interchangeably through this text.
- 9.
Hint: Output the values as CSV and use Excel to generate the plot.
- 10.
This distance is known, colloquially, as the “key hole.”
- 11.
The official name is TPK (telescope pointing kernel). These often-used nicknames refer to: a sub-package for conducting and analyzing multiple-star pointing tests (tpoint), the primary authors (Pat Wallace and Dave Terret), and the library of subroutines, originally coded in Fortran, upon which much of this software package is built. (Little known trivia question: What does the “SLA” stand for in the now famous library “SLALIB”? Answer: Standard Library “A”.) Slalib can be obtained by sending email to ptw@tpsoft.demon.co.uk.
- 12.
For historical reasons, astronomers and engineers often use the term “tube” to refer to the telescope structure that holds the three large mirrors: pimary (or “M1”), secondary (or “M2), and tertiary (or “M3”).
- 13.
Plate scale is the number of pixels per arcsecond in this context. It can also refer to the number of pixels per millimeter, a value that depends only on the detector and not the optics that feed it, in other contexts.
- 14.
The term “offset” is not, strictly speaking, the correct term here, but for now we can think of it as an offset. See exercise 5 below for the full story on the difference between an offset and a “autoguider tracking error correction.”
- 15.
In broad terms a “point source” in astronomy just means a star. That is, a point of light that is not “fuzzy” like a distant galaxy, not a strange shape like an asteroid so big that it’s shape can be made out (i.e., is “resolved”), nor a big round planet like Jupiter.
- 16.
As with many terms adopted by software developers (e.g., “interface”), the word “centroid” has, by going outside the realm of strict grammatical correctness, been used to create a new verb, “centroiding,” by simply putting an “ing” on the end. The action would more correctly be called “computing the centroid,” and is also sometimes referred to as “computing the center of light,” or even, rarely, as “computing the center of mass” (since it employs a similar algorithm).
- 17.
Indeed, the iraf package for computing centroids supports over thirty tunable parameters (see section 4 in http://iraf.net/irafdocs/apspec.pdf).
- 18.
Depending on the algorithm, the value produced by the computation can actually vary widely for different combinations of box size and search center starting point. The Gaussian fit algorithm is the most robust in this regard (see Table 2). The issue of robustness with respect to these two initial conditions is taken up in exercise 1 below.
- 19.
The measurement of a star’s exact position is also a scientific endeavor, in which case even more elaborate software methods are used. This branch of astronomical science is called “astrometry.”
- 20.
By losing the star we mean it would fall outside the “capture range” of the guider system and the auto-guider, depending on how good the error handling is, would either (a) realize this and abort (good reaction) or (b) start “guiding on noise” and drive the telescope off into never-never land (bad reaction).
- 21.
In the section on pointing and tracking above (see Fig. 1) we provided the basic telescope mount types: az/el and equatorial. As specified there, effectively all professional telescopes (ground-based) are of the az/el variety so we restrict all following discussion in this text to telescopes of the az/el type.
- 22.
Extra credit exercise: Find a star coordinate, telescope latitude, and hour angle for which this is the correct conversion.
- 23.
A gain factor of 100 % is more typically expressed as a gain factor of 1.0; the convention being that gain is a value between 0.0 and 1.0. The 0.0 gain setting effectively “turns off the control loop,” but this can be useful as a quick method to “open the loop” without actually setting flags or stopping a process.
- 24.
Does a nearby star really move in exactly the same fashion; as though the two were connected by an invisible steel bar? Basically: Yes. Recall that any motion is due to Earth’s rotation and these objects are effectively infinitely far away. They do not move with respect to each other as would, for example, as you look out your train window, a nearby post and a more distant farm house do. They are more like two mountain peaks far in the distance that maintain their relative distance from one another independent of your motion on the train. But are there exceptions? Definitely; See non-sidereal tracking below.
- 25.
Strictly speaking, the assumption for auto-guiding basics was not just that the object be bright but that it also be “point-like.” As it turns out, most objects in the solar system, although they might appear as large disks or, in the case of asteroids, be strangely shaped, they have a uniform illumination pattern that autoguider centroid algorithms, broadly speaking, are happy with. The strange shapes that are difficult for auto-guider software to handle, and end up requiring the use of an offset guide star, are the “faint fuzzies”; i.e., galaxies. Bottom line: For this case, bright and slow, no special auto-guider techniques are required.
- 26.
Roughly speaking, ‘fast movers’ are those objects nearest the earth, like near earth asteroids and the earth’s moon. But, for different reasons, the motions of moons around nearby planets, like the Mars moons Deimos and Phobos, or even the satellites of Jupiter, Io and Europa, for example, can, in a relative sense, clip along as seen from Earth at certain points in their orbits and sometimes fall into this category. As do comets.
- 27.
Not a bright one like the KBO previously known as planet Pluto.
- 28.
The “steel bar" we referred to for that case is now a variable distance; more like a rubber band.
- 29.
Again, this is the total error (the ‘P’ of ‘PID’) before it has been reduced by the loop gain factor.
- 30.
A 10-s exposure on one of today’s large telescopes is on the long side, but would be necessary if the guide star is on the faint side. But this comes up frequently with solar system objects when observing in areas of the ecliptic tilted away from the galactic plane. And, moreover, for solar system objects, guide stars come and go, never the same on any two nights. A special term is used to refer to those times that a solar system object comes near a bright star (that can be used as a guide star, for example); the term is “appulse.” This should not be confused with an “occultation,” an event in which the solar system object actually overlaps the star location briefly (like an eclipse). An appulse refers to the star just coming nearby, but that is all that is necessary for auto-guiding purposes. Our 10 s exposure time is an indication that we are in a part of the sky without any particularly good appulse events.
- 31.
The term “star list” is colloquial and sometimes more correctly, but less romantically, referred to as the “target list.” In the last decade or so there has been a less than successful trend toward expanding the traditional “star list” to a more complex, XML structure called an “observing block.” There is hope for this approach, but for this text we restrict to the traditional star list mechansim.
- 32.
A star so near it could be reached within a lifetime without the benefit of extreme science fiction (No wormhole required!).
- 33.
The origin of this term “position angle” mode is as follows: The name given for the angle of the imaginary line connecting two stars in a binary pair is “position angle.” For example, the position angle of a pair in which one star is directly north of the other is either 0 or 180. The convention is to use the angle from brighter to fainter. So, as another example, the position angle of a binary whose faint member is due west of its brighter companion will be 270. Recall that these angles are expressed in the “looking up” handedness (i.e., east is left when north is up) which is flipped from the “looking down” handedness (i.e., east is right when north is up) we are familiar with seeing on maps of cities and roads on the Earth’s surface.
- 34.
What is the location of that point? Short answer: the optical axis. A common misconception you will hear is that this point is the “bearing axis” of the rotator mechanism. Not true. Certainly, if you spin the rotator at a rapid rotation rate during an exposure, that effect will dominate. But the “natural” field rotation that results from tracking the field as it arcs across the sky, knows nothing of the bearing axis location. Indeed suppose there were no rotator and hence no bearing axis; the bulls-eye effect would still result (centered about the optical axis). The trick of the pointing and tracking software is to contend with the misalignment of the bearing axis with the optical axis and this is no easy trick (just another reason to rely on a standard package like Wallace-Terret for this operation). As before, we cover the basics here since as a software professional working in the field of astronomy, you will write simple tools that address these problems, but at a lower level of precision; so it is valuable to have a fundamental grasp of the basics.
- 35.
If these terms, “telescope pupil” or “atmospheric dispersion” are not familiar, here is a quick explanation of their importance. Fixing the telescope pupil orientation is valuable for several observing modes used to achieve high angular resolution (see following section on adaptive optics). These include “aperture masking” and “angular differential imaging” (ADI). This latter technique, ADI, was used to take the first images of extra-solar planets (HR 8799 a and b). The benefit of fixing the direction of atmospheric dispersion (the effect that makes the Sun look like a big egg instead of a circular disk at sunset) comes in the post-processing of the spectra taken in this mode. After all, spectroscopy is all about dispersing the light, so keeping the path of that dispersion stable throughout an exposure can, intuitively, be seen as beneficial.
- 36.
At what rate will the stars rotate? They will rotate at the same rate as the “parallactic angle” (a term rarely used outside astronomy). For this reason, “vertical angle mode” is sometimes referred to as “parallactic angle mode.” Imagine two vectors each with their origin at the star you are observing. One vector points to the spot in the sky directly above your telescope (the “zenith”) and the other points at that point near the North Star called the north celestial pole (NCP). The angle between these two vectors is the parallactic angle.
- 37.
Not 100 % true, but, true “to first order.” There may be pointing model terms that require tweaking, but DO NOT APPLY these tweaks at the wrong point in your software. For example, do not apply these tweaks all at once as the object transits.
- 38.
Sill referred to as “the 200-inch.”
- 39.
It was discussed as early as 1638 in a publication by Galileo. The land of Liliput from Gulliver’s travel could not exist as a result of this law, and this example is often used when the square-cube law is presented.
- 40.
If you are an unusually tall person, you may also be aware that the square-cube law also comes into play in the manufacture of bicycle frames. You cannot simply “scale up” the original design.
- 41.
At its closest, Mars can actually be only about 150 times further than our Moon, but it can also get much, much further when it’s over there on the other side of the Sun. So for this example, we just choose a relatively close distance for Mars of about 77 million km, 200 times the distance to our moon.
- 42.
There are subtle variations on this equation. Often, for example, a factor of 1.22 is introduced. This is related to interference patterns, and something called “Airy rings” and other complexities required for a complete description of the intensity pattern formed by a point source on the focal plane of a telescope. But the basic relationships for understanding “seeing more clearly” are summarized in this simplified version. The reader interested in a deeper understanding of diffraction limited imaging is referred to [4].
- 43.
For a review of the definition of arcsecond visit the Target Planning section on page 6, and in particular, the text covering small angles.
- 44.
200,000 (or more precisely, 206,264.806) is a magic number in this game. See exercise 4 below to see why.
- 45.
Why is it so popular to use AO systems in the 1–5 micron range? Why not work in “the visible” (i.e., the narrow wavelength range we can see with our eyes)? At least half of the reason is technical. It is simply hard to build AO systems that work at wavelengths smaller than 1 micron; and there is no real advantage to building AO systems that work at wavelengths longer than 5 microns. Why is it hard to build AO systems that work at short, “visible,” wavelengths? As we will learn later in this section, AO systems use deformable mirrors that are re-shaped (by software, of course) a thousand times per second via tiny actuators. How tightly packed together can these actuators be clustered? The smaller the spacing, the shorter the correctable wavelength. This so-called “actuator pitch” is only, as of this writing, becoming tight enough to decrease the correctable wavelength of AO systems down into the visible range. What is the other half of the reason? That question is debated even as this textbook is being written. Some say, “This is where the interesting scientific studies can be carried out, at 1–5 microns.” Others say, “That is a selection effect; AO science cases are popular in 1-5 microns because that is where it is possible to carry them out.” At the time of this writing, AO systems that correct visible wavelengths are just coming on line. In a few years we will see if visible AO takes over; but, for now we assume K-band for all examples covered here.
- 46.
The 1–5 micron range is further divided between 1–3 microns versus 4–5 microns. The latter contains two bands, L-band and M-band, which are very useful for some of today’s more exciting science cases (studying the atmospheres of other planets, for example), but are not quite so popular for AO for two reasons: thermal background and the resolution is not so dramatically improved with AO. On the other side of K-band, the shorter wavelengths down in the 1–2 micron range, called J-band and H-band, are increasingly popular for AO, but more challenging technically. K-band has emerged as the “Goldilocks,” not too short and not too long, wavelength most popular for today’s AO systems.
- 47.
Also called “Fried cells” the 40 cm varies and is called either “\(\mathrm{R}_{0}\)” (pronounced R-nought), “Fried parameter,” or the “coherence length”. The coherence length only reaches 40 cm on exceptional nights. A value between 10 and 20 is more typical.
- 48.
Like alt/az telescope control, the AO WFC requires only the “PI” and in simple cases only the P of a “PID” control loop, not the “D.”
- 49.
Wavefront sensors come in three varieties. All three have a detector (95 % CCD and 5 % infrared and with the latter gaining ground on the former), but only two of these three generate “slopes.” These are called: Shack-Hartman, pyramid, and curvature. It is the first two of these three, Shack-Hartman and pyramid, that produce slopes and it is to these two that we limit our discussion in this text.
- 50.
Field Programmable Gate Array / Digital Signal Processor.
- 51.
Graphical Processing Unit.
- 52.
Again, we restrict our discussion here to Shack-Hartman and pyramid WFS (which will be described soon). Curvature sensors do not use quad-cells, but are rare (and becoming rarer).
- 53.
So called “extreme” AO tailored to planet hunting.
- 54.
This nearness to zero is referred to as the “wavefront residual error,” or just wavefront residual for short, and is a measure of how well our AO system is performing. In fact, there exists a formula to convert the wavefront residual to another measure of success called the “Strehl ratio.” We do not delve into these two figures of merit further in this text, but they are well-described in the literature (See [4]).
- 55.
The DM shape is formed by the actuator voltages vector.
- 56.
At the time of this writing, there exists a bias for North American AO systems to use zonal and for European AO systems to use modal. There is no obvious reason for this split other than historical inheritance.
- 57.
Interaction matrix (IM) is another name for the “inverse of the reconstructor.”
- 58.
Many details are omitted here that must be worked out from experience, and in consultation with the optical engineer assigned to your project. For example, to first produce a ‘flat’ DM requires a separate operation carried out with an interferometer. Also, there is an equipment safety issue here: A DM is expensive (usually about $200,000, but can in the case of an “adaptive secondary” or an extreme AO system, be much more). Depending on the type, ‘poking’ can, for example, tear the membrane. Most DM come with low-level electronics systems that protect against this, but it is best not to depend on this level of protection. The distance to ‘poke’ the actuator above the flat surface is best worked out in consultation with the optical engineer assigned to your project.
- 59.
The method and timing of this matrix inverse operation vary. Regarding the method, typically the matrix is not square and it is necessary to use one of the pseudo-inverse methods. Singular value decomposition (SVD) is the most popular (see reference [6]). Regarding the timing, some AO systems have a pupil that rotates (see vertical angle mode in the rotator section above). In this case, the reconstructor may have to be re-computed every few degrees of rotation. Even on today’s fast computers this re-computation, which includes the pseudo-inverse operation, cannot occur at 1,000 Hertz.
- 60.
Why should tight coupling with TCS so dramatically increase the complexity of, for example, the control software for an instrument de-rotator? The answer is more cultural than technical. Instruments are typically developed at “home institutions.” These are often universities or research institutes thousands of kilometers away from the telescope on which their instrument will be installed. The TCS is typically the responsibility of software engineers working on site at the telescope. The interface control documents and similar mechanisms for dealing with the geographically diverse teams are sufficient for most of the loosely coupled control systems, but, for more tightly coupled systems like instrument de-rotation, interface issues can be a problem.
- 61.
The best text for learning the basics of a CCD is still Janesick [7]. For the most part this text covers only the physics and electrical properties of a CCD, but some aspects of read-out software can also be found in this excellent text.
- 62.
Occasionally these two worlds overlap. Consider for example, an infrared camera pointed at the reflective slit jaws of an infrared spectrograph. The NIRSPEC instrument at WMKO stands as an example of this situation. This camera can be used both as a guider (fast exposures) or a science device (slow exposures). But this case is the exception and not the rule.
- 63.
The efficiency of the transfer varies from chip to chip (and is one of the quality measures: CTE = charge transfer efficiency), but is generally quite high. Usually more than 99.99%.
- 64.
The notion to use water as an analogy to charge is common in CCD nomenclature; for example, when half of the dynamic range of the charge capacity has been reached, CCD users commonly refer to this as “half of full well”.
- 65.
Observations are either “read-noise limited” or “background limited.” In the latter case, an observer can afford to read out the detector in a high noise configuration, but not in the former.
- 66.
This ROI feature is now becoming available on infrared detectors as well. In fact, the “R” in the name of one of the most popular infrared detectors in use for astronomical instruments at the time of this writing, the “Hawaii 2-RG” stands for ROI (region of interest). But it is used far less frequently than the ROI features of CCDs, which have been in popular use for decades in auto-guiders, so we do not address the infrared ROI case in this text. Why is the ROI feature of infrared detectors less popularly used than it is for CCD technology? The most popular use for ROI is for auto-guiders and these are typically implemented with CCD technology.
- 67.
Apologies for the pun.
- 68.
Possibly the most famous application of drift scan can be found at the 2.5 m Sloan Digital Sky Survey Telescope on Apache Point. Two other facilities that make productive use of the drift scan method are the 0.9 m Spacewatch Telescope on Kitt Peak and the 1.2 m Oschin Schmidt/Palomar-Quest camera on Mount Palomar.
- 69.
For both CCD and infrared detectors, the readout software is typically “firmware” since it runs on a DSP or similar fast FPGA (bare bones, no operating system) device. Moreover, as of this writing the first “sidecar ASIC” systems are going into operation on several telescopes (typically spacecraft at this point). We will not cover these “no-software” read-out solutions here, but, as a software professional working in the field of software systems for astronomy, you should be familiar with these terms and trends.
- 70.
In reality, first, a “bias” level of “counts” or “data numbers” builds up in the read-out process that must be subtracted, ultimately, from the final, corrected image. Second, even while the shutter is closed and the CCD system is sitting patiently waiting for the next exposure to start, demon ‘dark current’ is building up in each pixel. But, the better the CCD, the lower the dark current. And sometimes it is negligible and can be ignored. OK, lots of new terms: “counts,” “data numbers,” “bias,” “dark current.” The first two are easy: these are just terms of art for the pixel values you get back from the read-out electronics (but we will now commonly use these terms throughout the text since they are commonly used in this field); the latter were covered in the section above on data reduction (see Fig. 1 in the Data and Data Archives chapter).
- 71.
We use the word “niche” here since often this programming is performed by individuals who are more electrical engineers than computer scientists and specialize in this area.
- 72.
It is more formally referred to as “MCDS” (multiple correlated double sampling), but calling it “Fowler mode” is certainly more catchy. This naming convention credits an early advocate of the technique, Al Fowler.
- 73.
CCD observers also apply the dithering technique on occasion, but far less frequently. Why less frequently? Two reasons: (a) the detectors are less subject to the artifacts that can pile up as systematic errors by staying in one spot on the chip and (b) due to the much lower background levels existing at the shorter, CCD, wavelengths, the exposures tend to be much longer. It is usually better when using a CCD to minimize read-out noise by making one read-out for, say, a 30 min exposure, rather than read 30 times by breaking it up into 1-min exposures just to allow dithering around on the chip.
- 74.
For logging, the unix syslog model is recommended. The syslog function is fast (thus avoiding those nasty bugs which change behavior when you raise the log level due to changes in the timing). All log messages are routed to syslogd, which yields anther useful feature: configurable redirection to files, other computers, email, cell phones, etc, via syslog.conf.
References
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A rigorous algorithm for telescope pointing, Patrick Wallace, SPIE 4848, 2002.
SLALIB/C Users Manual, Patrick Wallace, 2006.
Field Guide to Adaptive Optics, Robert Tyson and Benjamin Frazier, SPIE, 2004.
Dedicated flexible electronics for adaptive secondary control, Roberto Biasi et al, SPIE 5490, 2004.
Matrix Computations, Gene Golub and Charles Van Loan, JHU Press, 2004.
Scientific charge-coupled devices. SPIE Press, James Janesick, 2001.
Infrared Astronomy with Arrays, Ian S. Mclean, Kluwer Academic, 1994.
Data reduction and error analysis for the physical sciences, Philip R. Bevington and D. Keith Robinson, McGraw-Hill, 1969.
Design Patterns: Elements of Reusable Object-Oriented Software, Erich Gamma et al, Addison-Wesley, 1994.
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Conrad, A.R. (2014). Control Systems. In: Software Systems for Astronomy. SpringerBriefs in Astronomy. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7058-8_5
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