Warning, /education/kstars/doc/ekos-focus.docbook is written in an unsupported language. File is not indexed.

 <?xml version="1.0" encoding="UTF-8"?>
 <sect2 id="ekos-focus">
   <title>Focus</title>
 
   <indexterm>
     <primary>Tools</primary>
 
     <secondary>Ekos</secondary>
 
     <tertiary>Focus</tertiary>
   </indexterm>
 
   <sect3 id="focus-theory">
     <title>Theory Of Operation</title>
 
     <screenshot>
       <screeninfo> Ekos Focus </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="ekos_focus.png" format="PNG" width="75%"/>
         </imageobject>
 
         <textobject>
           <phrase>Ekos Focus</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> In order to focus an image, Ekos needs to establish a numerical
     method for gauging how <emphasis>good</emphasis> your focus is. It's easy
     when you look at an image and can see it as
     <emphasis>unfocused</emphasis>, as the human eye is very good at detecting
     that, but <emphasis>how</emphasis> can Ekos possibly know that? </para>
 
     <para> There are multiple methods. One is to calculate the Full Width at
     Half Maximum (FHWM) of a star profile within an image, and then adjust the
     focus until an optimal (narrower) FWHM is reached. The problem with FWHM
     is that it assumes the initial focus position to be close to the critical
     focus. Additionally, FWHM does not perform very well under low-intensity
     fluxes. An Alternative method is Half-Flux-Radius (HFR), which is a
     measure of the width in pixels counting from the center of the star until
     the accumulated intensity is half of the total flux of the star. HFR
     proved to be much more stable in conditions where you might have
     unfavorable sky conditions, when the brightness profile of the stars is
     low, and when the starting position of the focus is far from the optimal
     focus. </para>
 
     <para> After Ekos processes an image, it selects either a single star and
     starts measuring its HFR, or it selects a set of stars matching the
     criteria that have been set and calculates an average HFR. It can
     automatically select stars, or you can select a single star manually. It
     is recommended to allow Ekos to select a set of stars. </para>
 
     <para> Ekos supports 4 different focus algorithms: Iterative, Polynominal,
     Linear and Linear 1 Pass. </para>
 
     <itemizedlist>
       <listitem>
         <para> <emphasis role="bold">Iterative</emphasis>: In the Iterative
         algorithm, Ekos operates iteratively by moving in discrete steps,
         decided initially by the user-configurable step size and later by the
         slope of the V-Curve, to get closer to the optimal focus position
         where it then changes gears and performs smaller, finer moves to reach
         the optimal focus. The focus process stops when the measured HFR is
         within the configurable tolerance of the minimum recorded HFR in the
         process. In other words, whenever the process starts searching for a
         solution within a narrowly limited range, it checks if the current HFR
         is within % difference compared to the minimum HFR recorded, and if
         this condition is met then the Autofocus process is considered
         successful. The default value is set to 1% and is sufficient for most
         situations. The Step options specify the number of initial ticks the
         focuser has to move. If the image is severely out of focus, we set the
         step size high (i.e. greater than 250). On the other hand, if the
         focus is close to optimal focus, we set the step size to a more
         reasonable range (less than 50). It takes trial and error to find the
         best starting tick, but Ekos only uses that for the first focus
         motion, as all subsequent motions depend on the V-Curve slope
         calculations. Key features include:</para>
 
         <itemizedlist>
           <listitem>
             <para> The algorithm relies on the focuser having well controlled
             backlash. </para>
           </listitem>
 
           <listitem>
             <para> The algorithm can be fast using a minimum number of steps.
             </para>
           </listitem>
 
           <listitem>
             <para> The algorithm works on a "good enough" paradigm whereby it
             stops when the HFR is within % Tolerance of the perceived minimum.
             </para>
           </listitem>
         </itemizedlist>
       </listitem>
 
       <listitem>
         <para> <emphasis role="bold">Polynomial</emphasis>: In the Polynomial
         algorithm, the process starts off in Iterative mode, but once we cross
         to the other side of the V-Curve (once HFR values start increasing
         again after decreasing for a while), then Ekos performs quadratic
         curve fitting to find a solution that predicts the minimum possible
         HFR position. Key features include:</para>
 
         <itemizedlist>
           <listitem>
             <para> The algorithm relies on the focuser having well controlled
             backlash. </para>
           </listitem>
 
           <listitem>
             <para> The algorithm can be fast using a minimum number of steps.
             </para>
           </listitem>
 
           <listitem>
             <para> The algorithm uses curve fitting to pinpoint the optimum
             focus position. </para>
           </listitem>
         </itemizedlist>
       </listitem>
 
       <listitem>
         <para> <emphasis role="bold">Linear</emphasis>: In the Linear
         algorithm, Ekos steps outward from its starting point then moves
         inward taking regular datapoints through the point of optimum focus
         and then further inward, to draw a V-Curve. It then fits a quadratic
         curve to the datapoints and calculates the point of optimum focus. It
         then moves out again past the point of optimum focus, halves the
         stepsize and moves in again for a second pass. It looks to follow the
         curve from the first pass and find the minimum HFR. Due to randomness
         in the HFR measurements it uses the % tolerance to help decide when it
         has found a solution. Key features include: </para>
 
         <itemizedlist>
           <listitem>
             <para> The algorithm compensates for focuser backlash and can deal
             with both consistent and inconsistent backlash. </para>
           </listitem>
 
           <listitem>
             <para> The algorithm is slow, taking 2 passes to identify optimum
             focus. </para>
           </listitem>
 
           <listitem>
             <para> The algorithm uses curve fitting to pinpoint the optimum
             focus position in pass 1, but then uses % Tolerance to try to stop
             as close as possible to this HFR on pass 2. </para>
           </listitem>
 
           <listitem>
             <para> The algorithm is highly configurable with user control over
             many parameters like step size and number of steps. </para>
           </listitem>
         </itemizedlist>
       </listitem>
 
       <listitem>
         <para> <emphasis role="bold">Linear 1 Pass</emphasis>: In the Linear 1
         Pass algorithm, Ekos initially performs like the Linear algorithm in
         establishing the first pass V-Curve and fitting a curve to it to find
         the solution. Then, however, it moves directly to the calculated
         minimum. Key features include: </para>
 
         <itemizedlist>
           <listitem>
             <para> The algorithm compensates for focuser backlash, providing
             that backlash is consistent. </para>
           </listitem>
 
           <listitem>
             <para> The algorithm is fast, taking 1 pass to identify optimum
             focus. </para>
           </listitem>
 
           <listitem>
             <para> The algorithm uses more sophisticated curve fitting to
             pinpoint the optimum focus position. </para>
           </listitem>
 
           <listitem>
             <para> The algorithm is highly configurable with user control over
             many parameters like step size and number of steps. </para>
           </listitem>
         </itemizedlist>
       </listitem>
     </itemizedlist>
   </sect3>
 
   <sect3 id="optical-train-group">
     <title>Optical Train Group</title>
 
     <screenshot>
       <screeninfo> Optical Train </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="optical_train_group.png" format="PNG"
                      width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Optical Train Settings</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> The Optical Train group displays the currently selected Optical
     Train. By default this will be the primary imaging train, but other trains
     can be selected. The group consists of:</para>
 
     <itemizedlist>
       <listitem>
         <para> <guibutton>Train</guibutton>: The Optical Train currently in
         use by the Focus tab. Hover the mouse over this field for a more
         detailed description of the selected train.</para>
       </listitem>
 
       <listitem>
         <para> <guibutton>Edit Button</guibutton>: Brings up the Optical Train
         dialog to view and potentially change the optical trains.</para>
       </listitem>
     </itemizedlist>
   </sect3>
 
   <sect3 id="focus-focuser-group">
     <title>Focuser Group</title>
 
     <screenshot>
       <screeninfo> Focuser Settings </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focuser_group.png" format="PNG" width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focuser Settings</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> All INDI-compatible focusers are supported. It is recommended to
     use <emphasis role="bold">absolute</emphasis> focusers for the best
     results since their absolute position is known on power up. In INDI, the
     focuser <emphasis>zero</emphasis> position is when the drawtube is
     <emphasis role="bold">fully retracted</emphasis>. When focusing
     <emphasis>outwards</emphasis>, the focuser position increases, while it
     decreases when focusing <emphasis>inwards</emphasis>. The following
     focuser types are supported: </para>
 
     <itemizedlist>
       <listitem>
         <para> <emphasis role="bold">Absolute</emphasis>: Absolute Position
         Focusers such as RoboFocus, MoonLite, ASI ZWO </para>
       </listitem>
 
       <listitem>
         <para> <emphasis role="bold">Relative</emphasis>: Relative Position
         Focusers. </para>
       </listitem>
 
       <listitem>
         <para> <emphasis role="bold">Time Based</emphasis>: Time based
         focusers with no position feedback that adjust focus position by
         moving for a certain amount of time. </para>
       </listitem>
     </itemizedlist>
 
     <para> Start off by selecting the Focuser from the dropdown. </para>
 
     <para> For absolute focusers, you can set the ticks count in the Initial
     Steps Size field in the <link linkend="focus-mechanics">Mechanics</link>
     tab. For absolute and relative focusers, the step size is in units of
     <emphasis>ticks</emphasis> and for simple, or time based, focusers, the
     step size is in <emphasis>milliseconds</emphasis>. The
     <guibutton>In</guibutton> and <guibutton>Out</guibutton> buttons can then
     be used to move the focuser by this number of ticks.</para>
 
     <para> The Steps fields will initially contain the starting point in ticks
     for the focuser. As the focuser moves, the left field will update to
     reflect the focuser's current position. The right field will initially
     contain the starting position of the focuser but will update each time a
     successful Autofocus run completes, to keep a last good focus position. In
     addition you can set the right field to whatever value you like, and use
     the <guibutton>Goto</guibutton> button to move the focuser to this
     position.</para>
 
     <para> The <guibutton>Goto Focus Position</guibutton> button moves the
     focuser to the position in the righthand Steps field. </para>
 
     <para> The <guibutton>Stop Focuser Motion</guibutton> button stops the
     in-progress focuser motion. </para>
 
     <para> The <guibutton>Auto Focus</guibutton> button starts an Autofocus
     run. The <guibutton>Stop</guibutton> button is used to stop the run.
     </para>
 
     <para> The <guibutton>Capture Image</guibutton> button will take a frame
     based on the current settings in the <guilabel>CCD and Filter
     Wheel</guilabel> group. The <guibutton>Start Framing</guibutton> button
     will start repeatedly capturing frames until the
     <guibutton>Stop</guibutton> button is pressed. </para>
 
     <para> Some of the focus algorithms will attempt to cope with being
     started away from the point of optimum focus, but for predictable results,
     it is best to start from a position of being approximately in focus. For
     first time setup, <guibutton>Start Framing</guibutton> can be used along
     with the <guibutton>In</guibutton> and <guibutton>Out</guibutton> buttons
     to adjust the focus position to roughly minimize the HFR of the stars in
     the captured images. When Framing is used in this way, the <link
     linkend="focus-v-curve">V-Curve</link> graph changes to show a time series
     of frames and their associated HFRs. This makes the framing process much
     easier to perform.</para>
 
     <para> If you are completely new to astronomy, it is always a good idea to
     get familiar with your equipment in daylight. This includes getting the
     approximate focus position on a distant object. This will provide a good
     starting position for focusing on stars when nighttime comes.</para>
   </sect3>
 
   <sect3 id="focus-ccd-filter-wheel">
     <title>Camera &amp; Filter Wheel Group</title>
 
     <screenshot>
       <screeninfo> Focus Camera &amp; Filter Wheel Group </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focus_ccdfw_group.png" format="PNG" width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focus Camera &amp; Filter Wheel Group</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> This section of parameters deals with the Camera and Filter
     settings to use when focusing.</para>
 
     <para> The top row of controls allows CCD parameters to be set.</para>
 
     <itemizedlist>
       <listitem>
         <para> <guilabel>Exp</guilabel>: The exposure time in seconds.</para>
       </listitem>
 
       <listitem>
         <para> The <guibutton>Toggle Full Screen</guibutton> button pops the
         window displaying the focus frame out to a separate window. Pressing
         it again returns it within the focus window.</para>
       </listitem>
 
       <listitem>
         <para> The <guibutton>Show in FITS Viewer</guibutton> button pops-up a
         separate FITS Viewer window to display the focus frame, in addition to
         the focus frame displayed within the focus window.</para>
       </listitem>
 
       <listitem>
         <para> The <guibutton>Live Video</guibutton> button brings up the
         associated popup.</para>
       </listitem>
     </itemizedlist>
 
     <para> The next row of controls allows Camera parameters to be set. Choose
     a value from the binning dropdown and then set either the camera gain or
     ISO.</para>
 
     <itemizedlist>
       <listitem>
         <para> <guilabel>Binning</guilabel>: Increasing the binning will
         change the image scale as well as resulting in brighter pixels. A good
         place to start would be 1x1 and then see whether better results can be
         obtained by binning at higher levels such as 2x2 or 4x4.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Gain</guilabel>: Set the Gain for the Camera being
         used to focus. The value needs to be high enough to give a clear star
         pattern but not so high as to create too much noise to interfere with
         the focus operation. Some experimentation will be required to find an
         optimum value. If you are unsure where to start try unity gain for
         your camera and adjust from there.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>ISO</guilabel>: Set the ISO for the Camera being used
         to focus. Some experimentation will be required to find an optimum
         value.</para>
       </listitem>
     </itemizedlist>
 
     <para> The third row of controls deals with the Temperature Source and
     Filter, if there is one:</para>
 
     <itemizedlist>
       <listitem>
         <para> <guilabel>TS</guilabel>: Select the temperature source from the
         dropdown. Underneath are displayed the current temperature from the
         selected temperature source and the change in temperature between when
         the last successful Autofocus run completed and the current
         temperature. It is common practice to redo focus after significant
         temperature changes that alter the telescope's focus point.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Filter</guilabel>: Select the filter to use.</para>
 
         <para>To start focusing it will probably be easier to select the
         filter that allows the most light through, for example the Lum filter.
         The <guibutton>Filter Settings</guibutton> button brings up the <link
         linkend="capture-filter-settings">Filter Settings</link> popup. This
         allows a number of parameters to be set per filter to be used during
         an Autofocus run which could be unattended so a user would not be
         available to set parameters at run time. Broadly these allow two types
         of focus runs:</para>
 
         <itemizedlist>
           <listitem>
             <para> <emphasis role="bold">Per Filter</emphasis>: When another
             module, for example, the Capture module requires a filter change,
             it is possible to automatically refocus for the new filter. The
             exposure to use for each filter is taken from the <link
             linkend="capture-filter-settings">Filter Settings</link> popup.
             This is very useful where, for example, narrowband filter require
             longer exposure times than broadband filters.</para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Lock Filter</emphasis>: It is
             possible to specify a Lock filter to use when it is required to
             focus another filter. For example, if a Red filter is used and an
             Autofocus run required, it is possible to run the Autofocus using
             the Lum filter and then, when complete, adjust the focus position
             by an Offset value corresponding to the predetermined focus
             difference between the Lum and Red filters. This is useful when,
             for example, it is difficult to focus some filters directly
             without excessively long exposure times. Note that this locked
             filter approach may also be used in the <link
             linkend="ekos-align">Alignment Module</link> whenever it performs
             a capture for astrometry.</para>
           </listitem>
         </itemizedlist>
       </listitem>
 
       <listitem>
         <para> <guibutton>Reset</guibutton> button will reset the focusing
         subframe to full frame.</para>
       </listitem>
     </itemizedlist>
   </sect3>
 
   <sect3 id="focus-settings">
     <title>Focus Settings</title>
 
     <screenshot>
       <screeninfo> Focus Settings </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focus_settings.png" format="PNG" width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focus Settings</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> Next are 3 tabbed panes of parameters. These parameters are
     retained between sessions. First up is the Settings pane.</para>
 
     <itemizedlist>
       <listitem>
         <para> <guilabel>Auto Select Star</guilabel>: Allow Ekos to select the
         focus star(s) from the image. If not selected then the user will have
         to manually select a star.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Dark Frame</guilabel>: Check this option to perform
         dark-frame subtraction. This option can be useful in noisy images,
         where a pretaken dark is subtracted from the focus image before
         further processing.</para>
 
         <para> Dark frames are used by Focus, Alignment and Guiding. See the
         Dark Library feature within the <link linkend="ekos-capture">Capture
         Module</link> for more details on how to setup Dark Frames.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>AF Backlash Comp</guilabel>: Check this option to
         have the Autofocus algorithm perform backlash compensation. This
         option is available when using the Linear and Linear 1 Pass
         algorithms. This field should be set together with the
         <guilabel>Backlash</guilabel> field. See the <link
         linkend="focus-mechanics">Focus Mechanics</link> section for more
         details.</para>
 
         <para>Backlash in the focuser setup is likely to a combination of
         backlash in the electronic focuser itself (e.g. in the gearing
         mechanism), in the binding of the electronic focuser to the telescope
         drawtube, and in the telescope drawtube's mechanism. Thus, each setup
         will have its own backlash characteristic.</para>
 
         <para> There are several things to consider when working out how to
         deal with backlash: <itemizedlist>
             <listitem>
               <para> <emphasis role="bold">No Backlash</emphasis>: If you are
               fortunate enough to have a setup with no backlash then it would
               make sense to set AF Backlash Comp off. It should work fine if
               AF Backlash Comp is on, but the AutoFocus routine will make
               unnecessary movements.</para>
             </listitem>
 
             <listitem>
               <para> <emphasis role="bold">Backlash Managed by
               Focuser</emphasis>: If your focuser had the ability to manage
               backlash itself then you can use this facility and turn off AF
               Backlash Comp. Alternatively, if it's possible, you could turn
               off the focuser's backlash facility and set AF Backlash Comp
               on.</para>
             </listitem>
 
             <listitem>
               <para> <emphasis role="bold">Backlash Managed by Device
               Driver</emphasis>: If your device driver had the ability to
               manage backlash itself then you can use this facility and turn
               off AF Backlash Comp. Alternatively, if it's possible, you could
               turn off the device driver's backlash facility and set AF
               Backlash Comp on.</para>
             </listitem>
           </itemizedlist> </para>
 
         <para>It is important to have backlash managed in one place to avoid
         conflicts.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Sub Frame</guilabel>: Either use the Full Field of
         the camera or select a Subframe around the focus star during the
         Autofocus procedure. This is only relevant if a single star is used
         for focusing. Enabling subframing can speed up the focus
         process.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Box</guilabel>: Sets the box size used to enclose the
         focus star when using <emphasis role="bold">Sub Frame</emphasis>.
         Increase if you have very large stars. For Bahtinov focus the box size
         can be increased even more to better enclose the Bahtinov diffraction
         pattern.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Full Field</guilabel>: Either use the full field of
         the camera or select a Sub Frame around the focus star during the
         Autofocus procedure. If using multiple stars then this option must be
         selected.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Annulus</guilabel>: Used in conjunction with Full
         Field, Annulus provides two input fields that together define a
         doughnut over the FOV of the camera. Stars falling outside of the
         doughnut are discounted from processing. Setting an inner value above
         0% causes stars in the centre of the FOV to be discarded. This could
         be useful to avoid using stars in the target of the image (for example
         a galaxy) for focusing purposes. Setting an outer value below 100%
         causes stars in the edges of the FOV to be discarded during focusing.
         This could be useful if you do not have a flat field out to the edges
         of your FOV.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Suspend Guiding</guilabel>: Set this option to
         suspend guiding during an Autofocus run. An additional check is made
         to only suspend guiding if it is being carried out via the primary
         scope, for example when using an Off Axis Guider. The purpose of this
         is to prevent guiding from having problems with defocused stars during
         the focus process.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Settle</guilabel>: This option is used in conjunction
         with <guilabel>Suspend Guiding</guilabel>. It allows any vibrations in
         the optical train to settle by waiting this many seconds after the
         Autofocus process has completed, before restarting guiding.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Use Weights</guilabel>: This is an experimental
         option only available with the Linear 1 Pass focus algorithm and Curve
         Types of Hyperbola and Parabola. It requires Full Field to be
         selected. The option calculates the standard deviation of star HFRs
         and uses the square of this (mathematically the variance) as a
         weighting in the curve fitting process. The advantage of this is that
         datapoints with less reliable data and therefore larger HFR standard
         deviations will be given less weight than more reliable datapoints. If
         this option is unchecked, and for all other curve fitting where the
         option is not allowed, all datapoints are given equal weight in the
         curve fitting process. </para>
 
         <para> See the <link linkend="Levenberg-Marquardt">Levenberg-Marquardt
         Solver</link> for more details.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>R² Limit</guilabel>: This is an experimental option
         only available with the Linear 1 Pass focus algorithm and Curve Types
         of Hyperbola and Parabola. As part of the Linear 1 Pass algorithm, the
         degree to which the curve fits the datapoints, or <link
         linkend="Coefficient_of_Determination">Coefficient of Determination,
         R²</link>, is calculated. This option allows a minimum acceptable
         value of R² to be defined that is compared to the value obtained from
         the curve fitting process. If the minimum value has not been achieved
         then Autofocus will rerun. Only one rerun will be performed and even
         if the minimum R² has not been met the second time, the Autofocus run
         will still be deemed successful.</para>
 
         <para> Experiment to find an appropriate value but a good starting
         point would be 0.8 or 0.9</para>
       </listitem>
     </itemizedlist>
   </sect3>
 
   <sect3 id="focus-process">
     <title>Focus Process</title>
 
     <screenshot>
       <screeninfo> Focus Process </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focus_process.png" format="PNG" width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focus Process</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> This is the Focus Process parameters pane.</para>
 
     <itemizedlist>
       <listitem>
         <para> <guilabel>Detection</guilabel>: Select star detection
         algorithm. Each algorithm has its strengths and weaknesses. It is
         recommended to keep the default value, SEP, unless it fails to
         properly detect stars. The following are available:</para>
 
         <itemizedlist>
           <listitem>
             <para> <emphasis role="bold">SEP</emphasis>: Source Extraction and
             Photometry built in library. This is the default value.</para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Centroid</emphasis>: An extraction
             method based on estimating star mass around signal peaks.</para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Gradient</emphasis>: A single source
             extraction model based on the Sobel filter. </para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Threshold</emphasis>: A single source
             detection algorithm based on pixel values. </para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Bahtinov</emphasis>: This detection
             method can be used when using a Bahtinov mask for focusing. First
             take an image, then select the star to focus on. A new image will
             be taken and the diffraction pattern will be analysed. Three lines
             will be displayed on the diffraction pattern showing how well the
             pattern is recognized and how good the image is in focus. When the
             pattern is not well recognized, the <emphasis>Num. of
             rows</emphasis> parameter can be adjusted to improve recognition.
             The line with the circles at each end is a magnified indicator for
             the focus. The shorter the line, the better the image is in
             focus.</para>
           </listitem>
         </itemizedlist>
       </listitem>
 
       <listitem>
         <para> <guilabel>SEP Profile</guilabel>: If the star detection
         algorithm is set to <emphasis>SEP</emphasis>, then choose a parameter
         profile to use with the algorithm. It is recommended to use the
         default 1-Focus-Default profile as a starting point.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Threshold</guilabel>: Threshold percentage value is
         used for star detection using the <emphasis>Threshold</emphasis>
         detection algorithm. Increase to restrict the centroid to bright
         cores. Decrease to enclose fuzzy stars.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Algorithm</guilabel>: Select the Autofocus process
         algorithm: </para>
 
         <itemizedlist>
           <listitem>
             <para> <emphasis role="bold">Iterative</emphasis>: Moves focuser
             by discreet steps initially decided by the step size. Once a curve
             slope is calculated, further step sizes are calculated to reach an
             optimal solution. The algorithm stops when the measured HFR is
             within <emphasis role="bold">Tolerance</emphasis> of the minimum
             HFR recorded in the procedure.</para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Polynomial</emphasis>: Starts with
             the iterative method. Upon crossing to the other side of the
             V-Curve, polynomial fitting coefficients along with possible
             minimum solution are calculated. This algorithm can be faster than
             a purely iterative approach given a good data set.</para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Linear</emphasis>: This algorithm
             builds a V-Curve with approximately <emphasis role="bold">Out step
             Multiple</emphasis> steps on each side of the minimum. Having
             built the V-Curve it then fits a quadratic equation to the curve
             (parabolic shape) and uses this to calculate the focuser position
             giving the minimum HFR. Having identified the minimum it then
             performs a 2nd pass halving the step size, recreating the curve
             from the 1st pass. It attempts to stop within <emphasis
             role="bold">Tolerance</emphasis> of the minimum HFR calculated
             during the 1st pass.</para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Linear 1 Pass</emphasis>: This
             algorithm starts in the same way as <emphasis
             role="bold">Linear</emphasis> building a V-Curve. Having built the
             V-Curve it then fits the <emphasis role="bold">Curve
             Fit</emphasis> type to the datapoints and then calculates the
             focuser position giving the minimum HFR. Having identified the
             minimum it then moves directly to that point in a way designed to
             neutralise backlash.</para>
 
             <para> This algorithm supports the older style Quadratic curve
             type as well as the newer <link
             linkend="Levenberg-Marquardt">Levenberg-Marquardt Solver</link>
             for Hyperbolic and Parabolic curves. It will also weight the
             datapoints in the curve fitting process if Use Weights is
             checked.</para>
           </listitem>
         </itemizedlist>
       </listitem>
 
       <listitem>
         <para> <guilabel>Effect</guilabel>: You may select an
         <guilabel>Effect</guilabel> filter to enhance the image for preview
         purposes. It is highly advisable to turn off any effects during the
         focusing process as it may interfere with HFR calculations. For DSLR
         cameras, you can change the ISO settings.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Tolerance</guilabel>: The tolerance percentage value
         is used to help decide when the Autofocus process stops in the
         <guilabel>Iterative</guilabel> and <guilabel>Linear</guilabel>
         algorithms. During the Autofocus process, HFR values are recorded, and
         once the focuser is close to an optimal position, it starts measuring
         HFRs against the minimum recorded HFR in the sessions and stops
         whenever a measured HFR value is within % difference of the minimum
         recorded HFR. Decrease the value to narrow the optimal focus point
         solution radius. Increase to expand solution radius. </para>
 
         <warning>
           <para> Setting the value too low might result in a repetitive loop
           and would most likely result in a failed Autofocus process. </para>
         </warning>
       </listitem>
 
       <listitem>
         <para> <guilabel>Kernel Size</guilabel>: The kernel size of the
         gaussian blur applied to the image before applying Bahtinov edge
         detection. Used when <emphasis role="bold">Detection</emphasis> is
         Bahtinov.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Average over</guilabel>: Number of frames to capture
         at each datapoint. It is usually sensible to start with 1 but
         increasing this will result in an averaging process over the star
         HFRs.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Sigma</guilabel>: The sigma of the gaussian blur
         applied to the image before applying Bahtinov edge detection. Used
         when <emphasis role="bold">Detection</emphasis> is Bahtinov.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Num. of rows</guilabel>: The number of lines
         displayed on screen when using a Bahtinov mask. Used when <emphasis
         role="bold">Detection</emphasis> is Bahtinov.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Curve Fit</guilabel>: The type of curve to fit to the
         datapoints. </para>
 
         <itemizedlist>
           <listitem>
             <para> <emphasis role="bold">Quadratic</emphasis>: Uses a
             quadratic equation using a linear style least squares algorithm
             supplied by GSL (GNU Science Library). This is, in effect, a
             parabolic curve.</para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Hyperbola</emphasis>: Fits a
             Hyperbola using a non-linear least squares algorithm supplied by
             GSL (GNU Science Library). See <link
             linkend="Levenberg-Marquardt">Levenberg-Marquardt Solver</link>
             for more details.</para>
           </listitem>
 
           <listitem>
             <para> <emphasis role="bold">Parabola</emphasis>: Fits a Parabola
             using a non-linear least squares algorithm supplied by GSL (GNU
             Science Library). See <link
             linkend="Levenberg-Marquardt">Levenberg-Marquardt Solver</link>
             for more details.</para>
           </listitem>
         </itemizedlist>
       </listitem>
     </itemizedlist>
   </sect3>
 
   <sect3 id="focus-mechanics">
     <title>Focus Mechanics</title>
 
     <screenshot>
       <screeninfo> Focus Mechanics </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focus_mechanics.png" format="PNG" width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focus Mechanics</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> This is the Focus Mechanics parameters pane.</para>
 
     <itemizedlist>
       <listitem>
         <para> <guilabel>Initial Step size</guilabel>: This sets the step size
         to be used by various focus algorithms. For absolute and relative
         focusers this is the number of ticks; for timer based focusers this is
         the number of milliseconds.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Max Travel</guilabel>: Puts bounds on the amount of
         travel from the current focuser position that is permitted by the
         Autofocus algorithms. The purpose is to protect the focuser from
         travelling too far and potentially damaging itself. On the other hand,
         the value needs to be big enough to allow sufficient focuser motion to
         permit the auto focus runs to complete.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Max Step size</guilabel>: Used by the Iterative focus
         algorithm to limit the maximum step size that can be used.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Backlash</guilabel>: All mechanical devices with
         gears suffer from backlash. In a typical focuser there will be a dead
         zone where changing direction (e.g. from “in” to “out”) results in
         movement of the focuser by a few ticks, but no actual movement of the
         optical train.</para>
 
         <para>The Linear 1 Pass algorithm (like the Linear algorithm) provides
         backlash compensation in the 2 places during an auto focus run when
         the focuser moves outwards:</para>
 
         <itemizedlist>
           <listitem>
             <para> The initial outward movement of Initial Step Size * Out
             Step Multiple at the start of the run.</para>
           </listitem>
 
           <listitem>
             <para> When the inward pass is complete and Ekos has determined
             the best focus position and moves outward to it.</para>
           </listitem>
         </itemizedlist>
 
         <para> Linear 1 Pass will extend (by x ticks) the outward movement,
         and then, as a separate movement it will move inward by x ticks. So it
         always approaches the desired position in an inward direction.</para>
 
         <para>There are 2 schemes that can be used:</para>
 
         <itemizedlist>
           <listitem>
             <para>Set Backlash to 0. Ekos will use a value of 5 * Initial Step
             Size.</para>
           </listitem>
 
           <listitem>
             <para>Set Backlash &gt; 0. EKOS will use this value in its
             backlash calculations. There will probably be instructions with
             your focuser for determining the value of Backlash. It is not
             necessary to set an exact value for either Linear or Linear 1 Pass
             to work correctly; all that is required is that the value set in
             Backlash is &gt;= the actual backlash value. For example, if you
             measure backlash and get a value around 100, any value &gt;=100
             will work equally well. For example, set Backlash = 200.</para>
           </listitem>
         </itemizedlist>
       </listitem>
 
       <listitem>
         <para> <guilabel>Settle</guilabel>: The number of seconds to wait,
         after moving the focuser, before starting the next capture. The
         purpose is to stop any vibrations in the optical train from affecting
         the next frame.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Out Step Multiple</guilabel>: Used by the Linear and
         Linear 1 Pass focus algorithms, this parameter specifies the initial
         number of outward steps the focuser takes at the start of a Autofocus
         run.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Capture Timeout</guilabel>: The amount of time in
         seconds to wait for a captured image to be received before declaring a
         timeout.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Motion Timeout</guilabel>: The amount of time in
         seconds to wait for the focuser to move to the requested position
         before declaring a timeout.</para>
       </listitem>
     </itemizedlist>
   </sect3>
 
   <sect3 id="focus-display">
     <title>Focus Display</title>
 
     <screenshot>
       <screeninfo> Focus Display </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focus_display.png" format="PNG" width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focus Display</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> The focus display, displays a FITS viewer window onto the frame
     taken during the focus process. It displays the
     <guilabel>Annulus</guilabel> values superimposed on the image. All the
     stars detected by Ekos based on the selected parameters, have their HFR
     value displayed next to the associated star. </para>
 
     <para> The window supports the following FITS viewer options (at the top
     of the window):</para>
 
     <itemizedlist>
       <listitem>
         <para> <guibutton>Zoom In</guibutton> and <guibutton>Zoom
         Out</guibutton>.</para>
       </listitem>
 
       <listitem>
         <para> <guibutton>Default Zoom</guibutton> and <guibutton>Zoom to
         Fit</guibutton>.</para>
       </listitem>
 
       <listitem>
         <para> <guibutton>Toggle Stretch</guibutton>: Toggle screen stretch on
         or off.</para>
       </listitem>
 
       <listitem>
         <para> <guibutton>Toggle Crosshairs</guibutton>: Toggle crosshairs on
         or off.</para>
       </listitem>
 
       <listitem>
         <para> <guibutton>Toggle Gridlines</guibutton>: Toggle pixel gridlines
         on or off.</para>
       </listitem>
 
       <listitem>
         <para> <guibutton>Toggle Stars</guibutton>: Toggle star detection on
         or off.</para>
       </listitem>
     </itemizedlist>
   </sect3>
 
   <sect3 id="focus-v-curve">
     <title>V-Curve</title>
 
     <screenshot>
       <screeninfo> Focus V-Curve </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focus_vcurve.png" format="PNG" width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focus V-Curve</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> The V-Curve displays focuser position (x-axis) versus
     Half-Flux-Radius (HFR) (y-axis). Each datapoint is drawn on the graph and
     represented by a circle with a number representing the datapoint. How many
     datapoints are taken and how the focuser moves is determined by the
     parameters chosen. </para>
 
     <para> For certain algorithms, Ekos will also draw a curve of best fit
     through the datapoints. If <guilabel>Use Weights</guilabel> is selected
     then error bars are indicated on each datapoint that correspond to the
     standard deviation in measured HFR value.</para>
 
     <para> Under the V-Curve a number of parameters are displayed:</para>
 
     <itemizedlist>
       <listitem>
         <para> <guilabel>HFR</guilabel>: Displays the star HFR for the most
         recent datapoint.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Stars</guilabel>: The number of stars used for the
         most recent datapoint.</para>
       </listitem>
 
       <listitem>
         <para> <guilabel>Iteration</guilabel>: The number of datapoints taken
         so far.</para>
       </listitem>
 
       <listitem>
         <para> <guibutton>HFR</guibutton>: Invokes the <link
         linkend="focus-relative-profile">Relative Profile</link> popup.</para>
       </listitem>
 
       <listitem>
         <para> <guibutton>Clear Data</guibutton>: Resets the V-Curve graph by
         clearing the displayed data.</para>
       </listitem>
     </itemizedlist>
 
     <para> When framing, the graph format changes to that of a "time series"
     where horizontal axis denotes the frame number. This is to aid you in the
     framing process as you can see how HFR changes between frames. </para>
 
     <screenshot>
       <screeninfo> V-Curve as timeseries</screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focus_vcurve_timeseries.png" format="PNG"
                      width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focus V-Curve Timeseries</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
   </sect3>
 
   <sect3 id="focus-relative-profile">
     <title>Relative Profile</title>
 
     <screenshot>
       <screeninfo> Focus Relative Profile </screeninfo>
 
       <mediaobject>
         <imageobject>
           <imagedata fileref="focus_relative_profile.png" format="PNG"
                      width="50%"/>
         </imageobject>
 
         <textobject>
           <phrase>Focus Relative Profile</phrase>
         </textobject>
       </mediaobject>
     </screenshot>
 
     <para> The relative profile is a graph that displays the relative HFR
     values plotted against each other. Lower HFR values correspond to narrower
     shapes and vice-versa. The solid red curve is the profile of the current
     HFR value, while the dotted green curve is for the previous HFR value.
     Finally, the magenta curve denotes the first measured HFR. This enables
     you to judge how well the Autofocus process improved the relative focus
     quality. </para>
   </sect3>
 
   <sect3 id="How_to_Setup_for_an_Auto_Focus_Run">
     <title>How to Setup for an Autofocus Run</title>
 
     <para> The exact settings that work best for a given astronomical setup
     need to be worked out by the user using trial and error, but this section
     gives some pointers. It uses the Linear 1 Pass algorithm:</para>
 
     <itemizedlist>
       <listitem>
         <para> Start near to focus by manually finding focus. Use the
         <guibutton>Start Framing</guibutton> option and manually adjust focus
         to get to approximate focus.</para>
       </listitem>
 
       <listitem>
         <para> Select Linear 1 Pass and your curve of choice, say Hyperbola.
         Select Use Weights.</para>
       </listitem>
 
       <listitem>
         <para> Make sure you are finding enough stars.</para>
 
         <itemizedlist>
           <listitem>
             <para> Start with the SEP star detection method and the
             1-Focus-Default profile unless you have reason to use a different
             setup.</para>
           </listitem>
 
           <listitem>
             <para> On the Settings tab, use Full Field (rather than Sub Frame)
             which will use many stars rather than just one. Select Auto Select
             Star to let the system select the stars to use.</para>
           </listitem>
 
           <listitem>
             <para> Make sure Annulus is set to use a large amount of frame to
             make use of as many stars as possible. Note that there may be
             other factors that prevent you using all of the field such as
             issues with an un-flat field in the corners of the sensor, but
             don’t overdo the restriction.</para>
           </listitem>
 
           <listitem>
             <para> Set the camera settings such as exposure, gain and binning
             such that you are getting a good number of stars. Its impossible
             to be prescriptive here but try for between 20 and 100 (obviously
             if your focal length and target can’t find that many then the
             process should still work but may be less optimal from a curve
             fitting perspective). As a suggestion start with 2 sec exposures,
             unity gain for your camera and 1x1 binning.</para>
           </listitem>
 
           <listitem>
             <para> Upping the exposure usually finds more stars (but makes the
             focus process longer). You can also try taking multiple frames at
             the same point by setting the Average Over field &gt; 1
             frame.</para>
           </listitem>
         </itemizedlist>
       </listitem>
 
       <listitem>
         <para> Setup the Mechanics tab.</para>
 
         <itemizedlist>
           <listitem>
             <para> Setup Backlash. See the Backlash section for more details
             but if you do not know the value for your equipment then set to
             0.</para>
           </listitem>
 
           <listitem>
             <para> Setup Max Travel. This should be appropriate for your
             focuser to prevent overextending it. It needs to be big enough to
             support the values set in Initial Step Size and Out Step Multiple.
             It will need a minimum of just over Initial Step Size * Out Step
             Multiple. If you can, set it to, say, double this.</para>
           </listitem>
 
           <listitem>
             <para> Settle. If your focuser causes vibration in the optical
             train then you need to set this value so that after moving, the
             system waits for Settle seconds before taking the next frame. Try
             moving the focuser then taking a few frames at the same position.
             If the first frame after movement has bigger HFRs than subsequent
             frames, then you probably need to up the value in Settle.</para>
           </listitem>
 
           <listitem>
             <para> Out Step Multiple. Start with 4 or 5. This will give you
             9-10 or 11-12 datapoints which is a good place to start. You need
             enough datapoints to form a curve, but the more you have the
             longer the process will take to complete.</para>
           </listitem>
 
           <listitem>
             <para> Initial Step Size. The following shows a “good curve”.
             There is significant movement in the HFR axis to clearly
             demonstrate the curve, in this case max HFR is about 2.2 whilst
             min is 0.75 which gives a max / min of about 3.</para>
 
             <screenshot>
               <screeninfo> Good Focus Curve </screeninfo>
 
               <mediaobject>
                 <imageobject>
                   <imagedata fileref="focus_good_focus.png" format="PNG"
                              width="50%"/>
                 </imageobject>
 
                 <textobject>
                   <phrase>Good Focus Curve</phrase>
                 </textobject>
               </mediaobject>
             </screenshot>
           </listitem>
 
           <listitem>
             <para> In contrast, the next picture shows an Initial Step Size
             that has been set too low. The HFR varies from about 0.78 to 0.72.
             Which gives a max / min just over 1. The other clue that this is a
             poor setup is that the Error Bar range is very large compared to
             HFR movement which means that the curve solver is drawing a curve
             through a lot of noise, which means the results will not be very
             accurate.</para>
 
             <screenshot>
               <screeninfo> Bad Focus Curve </screeninfo>
 
               <mediaobject>
                 <imageobject>
                   <imagedata fileref="focus_bad_focus.png" format="PNG"
                              width="50%"/>
                 </imageobject>
 
                 <textobject>
                   <phrase>Bad Focus Curve</phrase>
                 </textobject>
               </mediaobject>
             </screenshot>
           </listitem>
         </itemizedlist>
       </listitem>
     </itemizedlist>
   </sect3>
 
   <sect3 id="Coefficient_of_Determination">
     <title>Coefficient of Determination, R²</title>
 
     <para> The Coefficient of Determination, or R², is calculated in order to
     give a measure of how well the fitted curve matches the datapoints. More
     information is available <ulink
     url="https://en.wikipedia.org/wiki/Coefficient_of_determination">here</ulink>.
     This is an experimental feature that is available for the Linear 1 Pass
     focus algorithm. In essence, R² gives a value between 0 and 1, with 1
     meaning a perfect fit where all datapoints sit on the curve, and 0 meaning
     that there is no correlation between the datapoints and the curve. The
     user should experiment with their equipment to see what values they can
     obtain, but as a guide, a value above, say 0.8 would be a good fit.</para>
 
     <para> There is an option to set an “R² Limit” in the Settings tab of the
     Focus window that is compared to the calculated R² after the auto focus
     run has completed. If the limit value has not been achieved, then the auto
     focus is rerun.</para>
 
     <para> Setting an R² Limit could be useful for unattended observation if
     the focus run produces a bad result for a 1-off reason. Obviously if the
     reason is not transitory then rerunning will not improve anything.</para>
 
     <para> If the R² Limit is not achieved and the focus process is rerun, and
     again fails to achieve the R² Limit, then the focus run is marked as
     successful to avoid the process getting stuck rerunning auto focus
     forever.</para>
 
     <para> This feature is turned off by setting the R² Limit to 0.</para>
   </sect3>
 
   <sect3 id="Levenberg-Marquardt">
     <title>Levenberg–Marquardt Solver</title>
 
     <para> The Levenberg-Marquardt (LM) algorithm is used to solve non-linear
     least squares problems. The GNU Science Library provides an implementation
     of the solver. These resources provide more details: </para>
 
     <itemizedlist>
       <listitem>
         <para>
           <ulink url="https://en.wikipedia.org/wiki/Levenberg–Marquardt_algorithm"/>
         </para>
       </listitem>
 
       <listitem>
         <para>
           <ulink url="https://www.gnu.org/software/gsl/doc/html/nls.html"/>
         </para>
       </listitem>
     </itemizedlist>
 
     <para> The Levenberg-Marquardt algorithm is a new feature added for the
     Linear 1 Pass focus algorithm. It is a non-linear least-squares solver and
     thus suitable for many different equations. The basic idea is to adjust
     the equation y = f(x,P) so that the computed y values are as close as
     possible to the y values of the datapoints provided, so that the resultant
     curve fits the data as best as it can. P is a set of parameters that are
     varied by the solver in order to find the best fit. The solver measures
     how far away the curve is at each data point, squares the result and adds
     them all up. This is the number to be minimized, let's call it S. The
     solver is supplied with an initial guess for the parameters, P. It
     calculates S, makes an adjustment to P and calculates a new S1. Provided
     S1 &lt; S then we are moving in the right direction. It iterates through
     the procedure until:</para>
 
     <itemizedlist>
       <listitem>
         <para> the delta in S is less than a supplied limit (convergence has
         been reached), or</para>
       </listitem>
 
       <listitem>
         <para> the maximum number of iterations has been reached, or</para>
       </listitem>
 
       <listitem>
         <para> the solver encountered an error.</para>
       </listitem>
     </itemizedlist>
 
     <para> The solver is capable of solving either an unweighted or weighted
     set of datapoints. In essence, an unweighted set of data gives equal
     weight to each datapoint when trying to fit a curve. An alternative is to
     weight each datapoint with a measure that corresponds to how accurate the
     measurement of the datapoint actually is. In our case this is the variance
     of star HFRs associated with the datapoint. The variance is the standard
     deviation squared.</para>
 
     <para> Currently the solver is used to fit either a parabolic or a
     hyperbolic curve.</para>
   </sect3>
 </sect2>