This note was originally released before the release of the version 4 ROM upgrade to the ST-4.  The user should read this note in conjunction with the note dated November 25, 1991, which describes the new features introduced with the version 4 ROM.

Application Note
More on Tracking with the ST-4
October 10, 1990

This Application Note further describes the tracking capabilities of theST-4, and will elaborate on items which users have asked us about. While tracking can be a great aid when it works in a "point and shoot" fashion, it can also be a source of frustration when the particulars of the telescope or night confound you. The ST-4 goes to great lengths to make tracking a "point and shoot" operation, but you should understand how to use the power of the ST-4 to adapt to almost any combination of telescope, drive, etc. Hopefully the information in this note will supplement the material in the manual and give you the ability to use the ST-4 to the limits of its capabilities.

1. Buttons on the ST-4

This section describes the function of each of the buttons on the ST-4. This information has also been summarized on the attached Quick Reference Card which you may want to keep with the instrument.

INTERRUPT

Pressing (and holding) this button interrupts the ST-4 out of the repetitive Tracking and Find and Focus modes. You may have to hold this button down for several seconds to get the ST-4 to respond, and when interrupted, the red LED display on the ST-4 will read "HELLO".

MENU

Pressing this button when the ST-4 is displaying the "HELLO" message allows access to the user-configurable parameters affecting the operation of the instrument. Each of the parameters accessible through the MENU button are described individually in section 3. To return from the MENU functions back to the "HELLO" prompt requires cycling through each of the parameters by repetitively pressing the MENU key.

ADJUST

This button is used in conjunction with the MENU button described above for setting the user-configurable parameters. For each menu parameter, repetitively pressing the ADJUST button cycles through each of the allowed setting for that particular parameter. Pressing the MENU button selects the current setting of the parameter and advances to the next parameter.

TAKE DARK FRAME

Pressing this button when the ST-4 is displaying the "HELLO" prompt causes the ST-4 to take an exposure and store it in its internal memory. The terminology "dark frame" refers to an image void of light, and should betaken with the telescope covered up. Dark frames are discussed further in the next section.

FIND AND FOCUS

Pressing this button causes the ST-4 to repetitively take exposures until the INTERRUPT button is pressed. After each exposure, the Value, X, and Y displays are updated with the brightest object in the field of view's peak brightness (Value) and location on the CCD (X and Y). The Find and Focus mode is discussed further in the next section.

CALIBRATE DRIVE

Pressing this button causes the ST-4 to activate each of the relays in sequence to try to measure the telescope's correction speeds in the four directions (+RA, -RA, +Dec, Dec). The Calibrate mode is discussed further in the next section.

TRACK

Pressing this button causes the ST-4 to go into Tracking mode where the brightest object in the field of view is tracked such that it remains at a fixed position on the CCD. The Tracking mode is discussed further in the next section.

<- ->

Pressing any of the four arrow keys when the ST-4 is displaying the "HELLO" prompt causes a 0.2 second activation of the +X relay, +Y relay, X relay or Y relay. Also, pressing and holding any of the four arrow keys when the ST-4 is in the Find and Focus mode causes the appropriate relay to be activated for the length of time the button is held down. Note that in this mode it may take the ST-4 several seconds to respond to the button press as it finishes an exposure, but will then leave the relay activated until the button is released.

MODE and SELECT

These buttons provide no function at the current time and are reserved for use with future software enhancements to the ST-4.

2. ST-4 Operating Modes

This section describes each of the ST-4's stand-alone operating modes such as Find and Focus, Calibrate, and Tracking.

2.1. Taking Dark Frames

The purpose of a dark frame is to allow the camera to remove the effects of bias (a constant background level at the output of the CCD), "hot pixels", dark current, and other irregularities from the CCD which could otherwise be interpreted as visual information and adversely affect the tracking performance. By covering the telescope and pressing the TAKE DARK FRAME button the ST-4 takes an image as a dark frame and stores it into its internal memory (the ST-4 has enough memory for two images, a dark frame and a light frame). The ST-4 can then subtract that dark frame from each real image as it is captured, and remove these unwanted effects. This is especially important when you are tracking on dim stars; there is no good reason for not taking and using a dark frame.

Pressing the TAKE DARK FRAME button not only records the dark frame, but tells the ST-4 to then subtract that dark frame from subsequent images. This effect can be noted by a drop in the Value reading from some baseline level down to 0 after the dark frames are subtracted. Dark frames are dependent on the length of exposure as well as the settings of some other parameters from the MENU functions. When ever you change the EA, bA or b MENU parameters discussed in the MENU parameters section a new dark frame must be taken.

Note: A minor bug in cameras with serial numbers below 903000 causes those cameras to continue subtracting old/invalid dark frames even after the EA, bA or b MENU parameters have changed, and in fact will continue to subtract the old dark frame until a new one is taken or the camera is powered down. Cameras after that serial number will revert to not subtracting the dark frame after any of those parameters has changed until you have taken a new dark frame.

2.2. Find and Focus Mode

The Find and Focus mode is the mode the ST-4 powers-up into, continuously taking exposures and showing the brightness and position of the brightest object in the field of view. These three parameters (Value, X, and Y) are displayed as percentages. For example a Value reading of 50 indicates a peak brightness which is half the way towards saturating, and an (X,Y)reading of (25,90) indicates an object which is 1/4th across the CCD in X and 90% up the CCD in Y.

You can use the FIND AND FOCUS mode to focus the system by adjusting the focus until the Value reading is maximized when imaging on a star. You will be able to focus the system faster by choosing a bright star to focus on rather than trying to pick a dimmer star close to the area where you wish to do the tracking. This is due to the fact that you can use a much shorter exposure time and hence cycle through the focusing procedure faster. You should also be careful to allow the telescope to settle out after adjusting the focus knob because the residual vibrations will smear the star over several pixels reducing its peak brightness. Atmospheric turbulence ("seeing") can cause the Value to fluctuate considerably, so observe several readings when making a critical adjustment.

2.3. Calibrate Mode

The calibrate mode is provided so the ST-4 can measure the telescope's correction speed in terms of pixels per second. Knowing that, it can then determine the amount of time to activate a relay (engaging the drive) to correct for a given error in terms of pixels. In addition, the Calibrate mode determines the orientation of the CCD, measuring the direction of movement of a star across the CCD as each of the four relays is activated. Prior to using the Calibrate mode you should take a dark frame and approximately center a star in the field of view. The X and Y reading should be between 30 and 70. Also, it is not critical to calibrate on the intended tracking star, but you should choose one which is close in Declination. This is because the correction speeds in Right Ascension will vary with a star's Declination coordinate, being highest on the celestial equator and decreasing towards the poles.

Once setup, pressing the CALIBRATE DRIVE button causes the ST-4 to activate the +X, -X, +Y, and -Y relays in sequence. The star's position is measured and displayed. For sake of discussion lets call its position (X0,Y0). The +X relay is then activated for a fixed period of time T (set using the CA MENU parameter discussed in the next section), and the star's new position (X1,Y1) is measured and displayed. It then looks for the largest change in position X change (X1 - X0) or Y change (Y1 - Y0), and calculates the +X relay's correction speed and orientation (speed = X change / T or Y change / T, depending on which is larger). It then activates the -X, +Y and -Y relays in turn, measuring and displaying the new position, calculating the X change and Y change from the last position and the corresponding correction speed and orientation.

Errors can occur in the Calibrate mode from a variety of sources, and if the ST-4 detects any errors it will display error codes at the end of the calibration procedure. The error codes, E1 or E2, show for a second each and have a sub code of 1 through 4 indicating which relay the error was associated with (+X, -X, +Y and -Y respectively). Error code E1 indicates the ST-4 saw no perceptible motion of the star, and error code E2 indicates that while there was some movement, it was less than 5 pixels (2 to 3 display units) which was not great enough to use in determining the correction speed and that the ST-4 will not correct in those directions. This is not necessarily bad; it could be due to the fact that your telescope has no motor in declination, for example. Several other sources of error are described below:

CA needs adjustment:

If the CA parameter from the MENU is set too short for telescopes with slow correction speeds then the star will not move much and will cause errors. This can be detected by watching the X and Y display during the calibration procedure. To solve this you should increase the CA parameter from its default of 5 seconds to 10 or 20 and retry the calibrate procedure. You will not have to take a new dark frame to do this since increasing the CA parameter doesn't affect the exposure time but only increases the amount of the time the ST-4 activates each of the relays in the Calibrate mode. Similarly, if the CA parameter is set too high for telescopes with high correction speeds then the star may be moved off the CCD after activation of one or more of the relays. This can be detected by watching the Value display during the calibration procedure to make sure it remains relatively constant and doesn't drop dramatically after one of the moves. To solve this problem you should lower the CA parameter to 1 or 2 and retry the calibration procedure.

Star too near edge at start:

If the star is too near the edge of the CCD at the start of the calibration procedure then it may be driven off the CCD. This can be solved by re-centering the star and retrying the calibration procedure.

CCD head oriented improperly:

If the CCD head is oriented such that the motions caused by activating the X and Y relays causes the star to move along diagonal lines on the CCD then the calibration procedure will have difficulty. This can be solved by orienting the CCD head such that the CCD's X or Y axis is aligned with the Right Ascension or Declination axis. The alignment is not particularly critical and misalignments of 10° to 30° will cause little or no problem. The proper orientation can be determined by noting that the orientation of the CCD and the calibration sticker on the rear of the CCD head are identical, or by letting a star trail for a moment and observing the readout.

2.4. Tracking Mode

This section describes the details of the ST-4's Tracking mode. Prior to invoking the Tracking mode, you must first invoke the Calibrate mode to adjust the ST-4 to your telescope's performance.

When the TRACK button is first pressed, the ST-4 takes an initial image and finds and records the X and Y position of the brightest object in the field of view. It uses that initial position as the track-to or zero-error position. The ST-4 then cycles repeatedly, taking images, measuring the brightest object's position, calculating a tracking error which is the star's current position minus the track-to position, and making corrections to drive the star back to the track-to position.

At each pass through the tracking loop, the Value, X and Y displays are updated with the Average tracking error and Instantaneous X and Y tracking errors respectively. All errors are in terms of 0.2 pixel error units, meaning an error display of 1 corresponds to a tracking error of 0.2 pixels, a display of 5 units corresponds to an error of 1 pixel (5 * 0.2), etc. Independent of focal length, an error of 1 unit corresponds to a distance error of 3 microns or 1/8th of a mil. If errors greater than 9 units (1.8 pixels) occur, an E is displayed due to the limited size of the display. The Instantaneous X and Y errors (shown in the X and Y displays) tell what the star's error (actual position minus desired position) is at any one point in time, and can be either positive or negative. The Average error (shown in the Value display with an A in the first digit) is the average tracking error over the last 16 correction periods.

The way the ST-4 determines the star's current position and hence the tracking error is as follows: From the initial image, where the brightest object in the field of view was found, the ST-4 calculated that object's position using a centroid calculation in both X and Y. The centroid can be thought of as the "center of brightness", meaning if the brightness of a pixel corresponded to a physical weight, the object would be perfectly balanced if suspended from its centroid, with equal weight or brightness on all sides of the centroid position. Using the (X,Y) centroid of the brightest object in the initial image, the ST-4 then determines the coordinates of a 32 pixel x 32 pixel box centered on that centroid. This box is referred to as the tracking box, and represents a small subset of all the pixels in the 195 x 162 pixel CCD. On all subsequent images, theST-4 searches the tracking box for the brightest pixel, then calculates a 9x 9 centroid centered upon that bright pixel, and uses that as the star's current position. In addition, it checks to make sure the star's brightness has not fallen to one-half its initial value. If it has it will assume the star has been lost and not make any correction, and if it gets lost for 4 cycles in a row then the ST-4 activates the alarm relay. If, however, the star's brightness is ok, it calculates the tracking error(actual position minus desired position), and activates the necessary relays for the amount of time required to bring the star back to its zero-error position. It knows which relay and how long to activate it based upon the information it gathered in the Calibrate mode.

3. Menu Items

This section describes each of the user configurable parameters accessed through the MENU button.

EA - Exposure Adjust Parameter

The EA parameter controls the exposure time. The default is 1second and can be adjusted from 0.1 through 20 seconds. In Tracking mode, increasing the exposure time allows the ST-4 to work with dimmer stars at the expense of making fewer corrections in a given period of time. Shortening the exposure time on nights with good seeing will allow the ST-4to correct more often. On nights with medium seeing, increasing the exposure time to several seconds can improve the tracking since the camera will responds to the star's average position and not try to correct for atmospheric scintillation. Note that anytime you change the EA parameter you will have to take a new dark frame.

CA - Calibration Adjust Parameter

The CA parameter controls the period of time the ST-4 will activate each of the four relays in the Calibrate mode. The default is 5 seconds and can be adjusted from 1 through 20 seconds. As discussed above in the Calibrate Mode section, the CA parameter should be adjusted so there is several units of motion of the star in each of the directions where the telescope has a correction drive.

SA - Scintillation Adjust Parameter

The SA parameter allows you to control the ST-4's automatic correction speed adjust. The default value is 2 and can be adjusted from 1through 10 pixels. The way the parameter affects the tracking is as follows: If during the tracking procedure the ST-4 notices that it is constantly overshooting or undershooting when in tracking, it will increase or decrease the amount of time it corrects for a given error in an attempt to improve the tracking. The SA parameter sets how many pixels error theST-4 must make before it will try changing the correction. On nights with good seeing, a 2 pixel error is fairly large and you would want the ST-4 to try to adjust the correction times should it ever get 2 pixels off, and you might try setting the SA parameter to 1. On the other hand, if the seeing is poor and atmospheric scintillation is causing the star to jump around, you would not want the ST-4 thinking it was in error and changing the correction times if the error is just due to scintillation. In these cases you would want to raise the SA parameter. You may also wish to raise the SA parameter on telescopes with long focal lengths since on these systems the tracking resolution in arc seconds is greater. Setting the SA parameter to 10 effectively eliminates the possibility of the ST-4 changing the correction speed determined during calibration since a 10 pixel error is quite high.

bA - Brightness Adjust Parameter

The bA parameter has two settings, A for Average, and F for Faint. The Faint mode can improve tracking with dim stars (those with Value readings less than 10 with the b parameter set to 3 or 4 and any given setting of the EA parameters). The Faint mode works by smoothing the image prior to performing the tracking calculation which lowers the calculations sensitivity to random noise. Each pixel value in memory is replaced by the sum of the 3 x 3 box centered on that pixel. A stellar image is usually several pixels wide so that smoothing does not significantly degrade tracking accuracy while improving system performance to very faint stars by about 1 magnitude.

You will not want to use the Faint mode for bright tracking stars(those with Value readings above 10 to 15) because it will degrade the tracking performance. Also note that anytime you change the bA parameter you will have to take a new dark frame.

H1 & H2 - Hysteresis Parameters

In an ideal mechanical world, when you instructed your telescope to move up in Declination and then reverse and move down the telescope would move up at a constant rate and then when asked to reverse itself would instantly start moving down at a constant rate. Unfortunately the mechanical world is not ideal, and mechanical systems suffer from an effect called hysteresis or backlash. Hysteresis manifest itself at the turnaround point in our example above, and instead of the telescope reversing directions instantly, it may take several seconds for the telescope to reverse, in which time the telescope could be motionless while the gear system takes up slack, etc.

The presence of backlash or hysteresis in one or both of the motor drives for a telescope will not prohibit use with the ST-4. It will just cause the ST-4 to have to make several corrections to drive the star back to its desired position, but the star will eventually do so because any time it is away from its initial position the ST-4 knows it must drive it back. If, however, you can quantify the hysteresis of your drive then the ST-4can easily accommodate it by increasing the length of correction signal applied whenever the drive is asked to reverse the correction from the previous correction.

The way you measure the hysteresis associated with your telescope drive is to drive each of the axes in one direction long enough that the star is moving steadily, then measure the amount of time you must press the opposite button on your hand controller before the star starts moving back in the opposite direction. You can then set the H1 and H2 parameters to the turn-around time (in seconds) for the X and Y axes respectively. Note that the relationship between the X and Y axes (H1 and H2 parameters) and Right Ascension and Declination will depend on the orientation of the CCD head in the eyepiece holder. Also, the H1 and H2 parameters default to 0seconds and can be set anywhere n the range 0 through 3.0 seconds. The number displayed is the hysteresis time in tenths of a second.

Note:  The Calibrate mode does not measure the proper settings for the H1and H2 parameters. Also, you should be comfortable with your understanding of how the ST-4 works before worrying about fine-tuning the tracking with the H1 and H2 parameters

b - Boost Factor Parameter

The b parameter allows you to increase the ST-4's sensitivity when dim tracking stars are used (those with Value readings less than approximately 15). It does this by boosting the gain of the Analog to Digital converter used to convert the CCD's output voltage (representing integrated light) into digital numbers for processing. The default value is 1 and the parameter can also be set to 2, 3 or 4 where the gain is doubled, tripled and quadrupled respectively. Increasing the setting of the b parameter increases the ST-4's sensitivity. Increasing the boost factor can have an advantage over using the Faint mode in that a stars' image will not be fattened since a smoothing function is not applied. Note: Anytime you change the b parameter you will have to take a new dark frame.

4. Tracking Suggestions

This section contains hints or suggestions on how you can optimize the performance of the ST-4 as a star tracker. The comments are organized as a series of tradeoffs you will have to make, and the reasons for picking anyone set of parameter settings over another.

Star Brightness vs Exposure Time

The first parameter you will want to adjust to accommodate differing star brightnesses is the exposure time. Simply put, dimmer stars will require longer exposure times to build up a reasonable image. Short exposure times (a second or less) allow the ST-4 to make corrections rapidly, and don't give the telescope much time to drift between corrections. Unfortunately, in situations where the seeing is moderate, the ST-4 may become extremely active and try to correct for atmospheric scintillation. In these cases you will want to increase the exposure time to several seconds. This allows the ST-4 to respond to the star's average position which is a better representation. The detriment to long exposure times is that the ST-4 may have to correct for some fairly large drift errors due to the fact the telescope has a longer period of time to drift. This of course will depend on the particular telescope, mount, etc. Also, remember to take a new dark frame anytime you change the exposure time.

Star Brightness vs Boost Factor

For dim stars (those with Value readings less than 10) you should raise the boost factor (b parameter) until the desired track star has at least a Value reading of 10. If after setting the boost parameter to its maximum value of 4 the star is still too dim you should use the Faint mode of the Brightness Adjust parameter. Remember to take a new dark frame anytime you change the Boost Factor or the Brightness Adjust parameters. The ST-4 CCD temperature regulation is coarse, and the average background pixel value is temperature sensitive. Ambient temperature variations could cause some problems for exposures longer than 5 seconds with a boost of four. Allowing the ST-4 to stabilize for 10 minutes or so before guiding at the lower limits is necessary.

Star Brightness vs Brightness Adjust Parameter

For extremely dim stars (those with Value readings less that 10with a boost of 3 or 4) using the Faint mode of the Brightness Adjust parameter is required. It can also help when the seeing is moderate because it will also tend to average out the star's position. Do not use the Faint mode when the Value reading is above 20 though because it can degrade the tracking performance due to saturation.

Importance of Good Focus

For bright stars, the focus is not very critical since minor de-focussing will just spread the peak brightness of the star over several pixels, which the centroid calculation will handle adequately. Proper focus is important for dim stars however since the reduction in peak signal level will directly affect the signal to noise of the signal at these intensities due to such things as quantization noise in the A/D and random noise.

Star's Position on CCD

In tracking mode you should try to put the star within the 10 to 90percent points in X and Y on the display, but need not be as restrictive as with the Calibrate mode.

Importance of Measuring Hysteresis

The H1 and H2 parameters really are fine tuning of the ST-4'stracking performance on most telescopes, and you need not worry about them much. They are most important on telescopes with large amounts of backlash, on the order of several seconds. In any case, the ST-4 will eventually re-position the star, but it may take several cycles for theST-4 to accommodate the turn around.

Use with Long Focal Lengths

Long focal lengths (greater than 100 inches) can make the ST-4quite active as the atmospheric effects cause the star to jump around several pixels. In these cases you should consider using SBIG's screw-in focal reducer for the ST-4. Professional observatories with large, fasttelescopes should contact us for special ST-4 software.

5. ST-4 Eliminator Plug

After you have modified your hand controller to interface to the ST-4 you may need to either leave your ST-4 plugged in (it doesn't need to be powered on), or need to make an adapter to allow your system to work without the ST-4. The adapter plug simulates the four closed relay contacts in the ST-4 and assure the signals that would normally be connected in the absence of an ST-4 are connected. This is not necessary if your control buttons are normally open.