# Photometry of minor Solar System bodies

The major challange in photometry on minor Solar System bodies is the tracking of the moving object of interest in the view field. The matching procedure, as it is used for a variable star, would not work without modifications, because the object changes its position between the frames with respect to surrounding stars. Also, the stars moves between the frames, as a result of mechanical inaccuracy of a telescope mount and its clockdrive.

This chapter explains how to make a light curve of a moving object, such as a minor Solar System body. For a guide on making a light curve of stationary objects (variable stars or exoplanets) follow this link.

The procedure of making a light curve of a moving object is the same as the process in case of a variable star except the matching step. The matching process is different here; a user has to specify at least three frames, called `key frames` and mark the moving object on each of them.

## Before you start

Before you start the reduction of your own CCD frames, you may need to perform several pre-processing steps. Though it isn’t necessary, combining the several correction frames into so-called “master” ones is advisory, because it reduces the noise and makes the result more precise. The method of making master correction frames is described in separate chapters.

See also

Master-dark frame and Master-flat frame

## Creating a new project

First of all, we will create a new project. To begin with processing of a set of source frames, we create a new project. To do so, open the Project menu and activate the New item. A new dialog appears.

The dialog for making a new project.

Fill in a name that will be assigned to the project. Because the name of the file that keeps track of the data related to the project, the project file, is derived from the name, some characters cannot appear in the project name, do not use: / ? % * : | “ < and >.

The field Location shows a path to the directory where a new project will be created. Edit the path to change the location, you can also click the Browse button to select a directory in a separate dialog.

The dialog also displays a list of available profiles. A profiles provides an intial set of configuration parameters into a new project. When you confirm the dialog, you should be in the main window again now. The table of input files shown there is empty.

The main application window with the table of input files, now empty.

See also

New project (dialog) and Main window.

## Input files

Now, we are going to tell the program which files we are going to work on. These files are called the input files. Their list is displayed in the table in the main application window. When the application is closed, the list of files are saved to the disk and it is restored back when the program is launched again.

Supposing that the table now consists of files from your previous task, let’s get rid of them. Please, use Files ‣ Clear files to start a new task instead of just removing the files from the table. Besides the clearing the table of input files, this function resets all internal variables, too.

Now, we need to populate the table with the CCD frames we’re going to reduce. There are two methods how to achieve that - adding a individual files or adding all files from a folder. Which way is the best for you depends on organization of your observations on the disk. I’d suggest you to make a folder for each year, a folder for each night in it, the a subfolder for a name of object or another view field identification and finally a subfolder named upon the color filter (if you use more of them). In this case, the “Add frames from a folder” method is more convenient.

Click on Files ‣ Add frames from folder in the main menu. A new dialog appears. In the dialog, find a folder where the inputs files are stored in. Click on an entry in the Places pane to go to one of a preselected folders, double click in the middle pane enters the folder. The buttons in the upper part of the dialog shows your current position in the directory tree, you can use them to go to one of the parent folders. Enter the folder with the input files - you should see them in the middle pane. Then, click on the Add button to add files to the table of input files. The program shows the number of added files in the separate dialog. The Add frames from folder dialog is not closed automatically and allows a user to continue. Click on the OK button to close the dialog and return to the main window.

The “Add folder” dialog with the place selection box (left), the file selection box (right)

If you want to reduce only a subset of files from a folder, click on Files ‣ Add individual frames in the main menu. A new dialog appears, similar to the previous one. In the dialog, find a folder where the inputs files are stored in. Click on an entry in the Places pane to go to one of a preselected folders, double click in the middle pane enters the folder. The buttons in the upper part of the dialog shows your current position in the directory tree, you can use them to go to one of the parent folders. In the middle pane, select the files using the `Ctrl` modifier to include and exclude a single file and the `Shift` modifier to include a range of files. Then, click on the Add button to add selected files to the table of input files. The program shows the number of added files in the separate dialog. The Add individual frames dialog is not closed automatically and allows a user to continue. Click on the OK button to close the dialog and return to the main window.

The “Add files” dialog with the place selection box (left), the file selection box (middle) and the preview panel (right).

See also

Add frames from folder (dialog) and Add individual frames (dialog).

## Frame reduction

Reduction of CCD frames is a process that takes source CCD frames, performs their conversion and calibration, detects stars on each frame and mearures their intensity and finally finds correlation (match) between objects that were found in the data set. The process of reduction prepares the data that are necessary for making a light curve.

The reduction consists of several steps - conversion, calibration, photometry and matching. They can be invoked step-by-step manually. The preferred way is to use the Express reduction dialog that allows to perform these steps in a batch. Using the menu, activate the Reduce ‣ Express reduction item. A new dialog appears. The dialog has several options aligned to the left, Each of them relates to an optional step in the reduction process.

The dialog for setting parameters of the reduction process

Fetch/convert files

Check the Fetch/convert files. In this step, the program makes copy of the source CCD frames. This is necessary, because the following calibration steps will modify them and we don’t want the program to change our precious source data.

Dark-frame correction

A raw CCD frame consists of several components. By the calibration process, we get rid of those which affect the result of the photometry. In some literature, the calibration is depicted as the peeling of an onion. There are three major components which a raw frame consists of - the current made by incident light, current made thermal drift of electrons (so-called dark current) and constant bias level. In standard calibration scheme, which we will demonstrate here, the dark-frame correction subtracts the dark current and the also the bias. Because of the nature of the dark current, it is necessary to use a correction frame of the same exposure duration as source files and it must be carried out on the same CCD temperature, too. Thus, the properly working temperature regulation on your CCD camera is vital.

Flat-frame correction

Then, we have to compensate the spatial non-uniformity of a detector and whole optical system. These non-uniformities are due to the fabrication process of a CCD chip and they are also natural properties of all real optical components, lenses in particular. The flat-frame correction uses a flat-frame to smooth them away. The flat-frame is a frame carried out while the telescope is pointed to uniformly luminous area. In practice, this condition is very difficult to achieve, the clear sky before dusk is usually used instead.

Photometry

The photometry is a process that detects stars on a CCD frame and measures their brightness. Unlike the previous steps, the result is saved to a special file, so-called the photometry file. There are a lot of parameters which affect the star detection and also the brightness computation. In this example, the default values work fine, but I would suggest you to become familiar with at least two of them - FWHM and Threshold - before you start a real work. Check the Photometry option.

FWHM

  The FWHM parameter specify the expected width of stars on a frame. The value is the Full Width at Half Maximum in pixels. The parameter controls the behavior of the low-pass digital filter, which is used in the star detection algorithm.

Threshold

  The Threshold parameter specify the lowest brightness of detected stars. Fainter objects are considered to be background artifacts and thus sorted out. The value is dimensionless coefficient.

Once you tune up the parameter for your environment, usually it is not necessary to adjust them for every task, unless the quality of your images varies considerably. In the first iteration, you can use the default values (FWHM = 3.0 and Threshold = 4.0) and do the photometry. Click on the Reduce ‣ Photometry item in the main menu and confirm the new dialog by the OK. Then, by double click on a frame in the main window open the preview window and check the results. If there are stars which have been detected as a close binary although it is not true, you should increase the FWHM value. If the stars you are interested in are not detected, try decrease the Threshold value. If it doesn’t help, decrease the FWHM. If there is a lot of background artifacts detected as a real stars, increase the Threshold. By several iterations, adjust the parameters, so all the stars you are interested in are detected and there are no false binaries.

Matching (skipped)

In case of observation of moving object of intereset, do not perform the matching now; keep the Matching option unchecked. The matching process requires user input, but this can be done only when photometry of the source frames has been finished.

Invoking the reduction process

In previous steps, we have configured parameters of the reduction process and we are ready to start it. Click the OK button. During the execution a new window appears displaying the state of the process; all the information is also presented there. This window will be automatically closed after finishing the process. Wait for the process to finish.

The dialog displayed during time demanding operations.

After finishing, the icon in the file table changes; the information about the time of observation, the length of the exposition and the used filter is filled in. In case some of the frames could not be processed successfully, the entry is be marked with a special icon and in the Status column the error message is indicated.

The main application window after the photometry step

See also

Express reduction (dialog).

## Matching the frames and tracking the object of interest

The object is expected to move along a smooth curve in time. We pick up at least three frames, called key frames, and we mark the object of interest on each of the key frames. It is recommended to start with one key frame at the beginning, one key frame in the middle and one key frame at the end of the set. The key frames define three points and a curve is fitted between them. The curve is used to determine expected position of the object in observation time of any other frame and an unidentified object found on a non-key frame close to the expected position is matched as the object of interest.

Click on the Reduce ‣ Match stars item in the main menu. A new dialog appears.

The Matching dialog in the moving target mode

In the dialog, check the option Moving target (20). List of source frames is presented in the table (21). In the table, select a frame that will be used as the first key frame. The first key frame has got the same function as a reference frame in the matching process for stellar objects; all frames are matched against this frame and it is also used as a background in object selection dialogs. When you select a frame, it is shown in the preview area (22). Click the Add key frame button. A new dialog appears.

The Select target dialog

Find the object of interest and click on it (31). Confirm the dialog (32). You get back to the previous dialog. In the table of frames (21), the key frames gets an icon of a red key before the frame number (24).

Repeat this step until there are at least three key frames. The other key frames are marked by a white key icon (25). The red key icon indicates the frame that is used as a reference key frame in the matching process. Then, click on the Apply button to start the matching process.

The process now runs automatically. The selected key frames are processed first, the positions of the selected object of interest on the key frames are used to find the path which the object follows by fitting a polynomial function to them. Then, the rest of the frames are processed; the fit is used to find out an expected position of the object in an observation time and an object close to the expected position is marked as the object of intereset on the frame.

See also

Match stars (dialog)

## Making a light curve

Click on the Plot ‣ Light curve item in the main menu. A new dialog appears. The dialog allows you to set up the options for the light curve. If you want only a subset of frames from the project to be included in the curve, check the selected files only option in the box. The program can also include several corrections and coefficients to the output file, these features are discussed later in the text.

Confirm the dialog by the OK button.

The dialog for making a light curve.

See also

Plot light curve (dialog)

## Selecting the stars

The next dialog shows the reference frame and allows you to select the object of interest, the comparison and the check stars. All detected objects are highlighted. Click anywhere on the frame with the right mouse button to open a context menu. Select the item Set moving target as a variable. The object of interest is now drawn in red color and the label “var” is placed near to it (1). Pick up a star that shall be used as a comparison star and click on it using left mouse button. Select the item Comparison, the object is now drawn in green color and the label “comp” is placed near to it (2). I would recommend you to pick up also two check stars. Confirm the selection by the OK button (3).

The dialog for selection of an object of interest (red), a comparison star (green) and check stars (blue).

See also

Choose stars (dialog)

## Choosing an aperture

Now, we have to choose the aperture. You can image the aperture as a virtual circular pinhole, placed on each star on a frame to measure its brightness. All pixels that are inside the pinhole are included in computation leaving out the background pixels. The best aperture should be big enough to include most of the star’s light, on the other hand, the bigger aperture is used the more background is included and the more noisy the result is. Because of this, the photometry process computes the brightness of each star in a set of predefined apertures of radius in the range of 2 and 30 pixels.

To select the best aperture, we can take advantage of a comparison and check stars - providing that they are constant, we can compute the differential magnitudes between each couple of them on each other and then compute the variance or standard deviation from the mean level. For the best aperture, the deviations are minimal.

In the next dialog, the graph shows the standard deviation for each aperture. Find the aperture with the minimal deviation and click on it using the left mouse button. A context menu appears. Select the Select aperture item. The point is drawn in red color now and the label is placed near to it. Confirm the selection by the OK button.

The dialog for selection of an aperture.

See also

Choose aperture (dialog)

## Plotting a light curve

Now, the program has got enough information to make a light curve. It is presented in a new window which appears automatically.

The dialog with a light curve graph.

See also

Light curve (dialog)

## Trimming outliers from the curve

Is is possible to manually trim outlying observations from the curve. You can select an individual point by a right click, you can also select more than one point by pressing a Shift key and left mouse button and drawing a rectangle in the graph. Then, click the right mouse button on a point in the selection to open the context menu. There are two options: When you select the option delete from data set, the selected measurements are removed from the current light curve, the data will be shown when you make another light curve or Rebuild the actual curve. The other option remove from project means that the frames corresponding to the selected measurements are removed permanently from the list of input files (see: Main application window) and such measurements won’t be included in any other output. It is not allowed to remove a reference frame.

Note

CCD frames of 268 Adorea:
BlueEye600, RiLA 0.60-m f/5 Ritchey-Chretien + CCD G4-4000BI
(ProjectSoft HK & Astronomical Institute of the Charles University in Prague)