pmShutterCorrection.h

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/* @file pmShutterCorrection.h
 * @brief Functions to build and apply a shutter exposure-time correction.
 *
 * @author Eugene Magnier, IfA
 * @author Paul Price, IfA
 *
 * @version $Revision: 1.11 $ $Name:  $
 * @date $Date: 2007/01/24 02:54:15 $
 * Copyright 2006 Institute for Astronomy, University of Hawaii
 */

#ifndef PM_SHUTTER_CORRECTION_H
#define PM_SHUTTER_CORRECTION_H

/// @addtogroup detrend Detrend Creation and Application
/// @{

/*  A mechanical shutter may not yield uniform exposure times as a function of
 *  position on the detector.  The typical error consists of a constant
 *  exposure-time offset relative to the requested value, ie exposure time is
 *  T_o + dT(x,y).  The exposure error, dT, may be measured with the following
 *  scheme.  Obtain a set of exposures with different exposures times taken of
 *  the same flat-field source; the source must be spatially stable between the
 *  exposures, but need not have a stable amplitude.  For an illuminating flux
 *  of intensity F(x,y) = F_o f(x,y), the signal recorded by any pixel in the
 *  detector is given by: S(t,x,y) = F_o(t) f(x,y) (T_o + dT(x,y)) where F_o is
 *  the F_o(t) is the (variable) overall intensity of the illuminating source
 *  and f(x,y) is the spatial illumination patter times the flat-field response.
 *  Choose a reference location in the image (eg, the detector center) and
 *  divide by the value of that region (ie, mean or median):
 * 
 *  s(t,x,y) = S(t,x,y) / S(t,0,0)
 *  s(t,x,y) = F_o(t) f(x,y) (T_o + dT(x,y)) / F_o(t) f(0,0) (T_o + dT(0,0))
 *  s(t,x,y) = f(x,y) (T_o + dT(x,y)) / f(0,0) (T_o + dT(0,0))
 * 
 *  we can absorb the term f(0,0) into f(x,y) as we have no motivation for the
 *  scale of f(x,y).  For any single pixel, over the set of exposures, we thus
 *  need to solve for dT(x,y), dT(0,0), and f'(x,y) in the equation:
 *  s(t,x,y) = f'(x,y) (T_o + dT(x,y)) / (T_o + dT(0,0))
 * 
 *  we avoid directly fitting these values as the process would be a non-linear
 *  least-squares problem for every pixel in the image, and thus very time
 *  consuming.  There are linear options which may be used instead.
 *  First, as T_o goes to a large value, s() approaches the value of f'(x,y).
 *  Next, as T_o goes to a very small value, s() approaches the value of
 *  f'(x,y)*dT(x,y)/dT(0,0).  Finally, when s() has the value of
 *  f'(x,y)*(1 + dT(x,y)/dT(0,0))/2, T_o has the value of dT(0,0).  with data
 *  points covering a reasonable dynamic range, we can solve for these three
 *  values by interpolation and/or extrapolation.
 * 
 *  To take the strategy one step further, we could use the above recipe to
 *  obtain a guess for the three parameters and then apply non-linear fitting to
 *  solve more accurately for the parameters.  If we limit this operation to a
 *  handful of positions in the image (user defined, but the obvious choice would
 *  be positions near the center, edges, and corners), then we may determine a
 *  good value for dT(0,0).  Since there is only one dT(0,0) for the image, we
 *  can apply the resulting measurement to the rest of the pixels in the image.
 *  If dT(0,0) is not a free parameter, then the fitting process is linear in
 *  terms of dT(x,y) and f'(x,y)
 */

#include <pslib.h>

/// Shutter correction parameters, applicable for a single pixel
typedef struct
{
    double scale;                       ///< The normalisation for an exposure, A(k)
    double offset;                      ///< The time offset, dTk
    double offref;                      ///< The reference time offset, dTo
}
pmShutterCorrection;

/// Allocator for shutter correction parameters
pmShutterCorrection *pmShutterCorrectionAlloc();

/// Guess a shutter correction, based on plot of counts vs exposure time
///
/// This function is used before doing the full non-linear fit, to get parameters close to the true.  Assumes
/// exptime vector is sorted (ascending order; longest is last) prior to input.
pmShutterCorrection *pmShutterCorrectionGuess(const psVector *exptime, ///< Exposure times for each exposure
        const psVector *counts ///< Counts for each exposure
                                             );

/// Generate shutter correction based on a linear fit
///
/// Performs a linear fit to counts as a function of exposure time, with the reference time offset fixed (so
/// that the system is linear).  Performs iterative clipping, if nIter > 1.
pmShutterCorrection *pmShutterCorrectionLinFit(const psVector *exptime, ///< Exposure times for each exposure
        const psVector *counts, ///< Counts for each exposure
        const psVector *cntError, ///< Error in the counts
        const psVector *mask, ///< Mask for each exposure
        float offref, ///< Reference time offset
        int nIter, ///< Number of iterations
        float rej, ///< Rejection threshold (sigma)
        psMaskType maskVal ///< Mask value
                                              );

/// Generate shutter correction based on a full non-linear fit
///
/// Performs a full non-linear fit to counts as a function of exposure time.  The main purpose is to solve for
/// the reference time offset, so that future fits may be performed using linear fitting with the reference
/// time offset fixed.
pmShutterCorrection *pmShutterCorrectionFullFit(const psVector *exptime, ///< Exposure times for each exposure
        const psVector *counts, ///< Counts for each exposure
        const psVector *cntError, ///< Error in the counts
        const pmShutterCorrection *guess ///< Initial guess
                                               );

/// Measure a shutter correction image from an array of images
///
/// Given an array of readouts (with known exposure times from the cell concepts), this function measures the
/// shutter correction (our principal concern is for the time offset, rather than the normalisation) by
/// measuring the reference time offset using the full non-linear fit for a small number of representative
/// regions (middle and corners), and then using that to perform a linear fit to each pixel.
psImage *pmShutterCorrectionMeasure(const psArray *readouts, ///< Array of readouts
                                    int size, ///< Size of samples for statistics for non-linear fit
                                    psStatsOptions meanStat, ///< Statistic to use for mean
                                    psStatsOptions stdevStat, ///< Statistic to use for stdev
                                    int nIter, ///< Number of iterations
                                    float rej, ///< Rejection threshold (sigma)
                                    psMaskType maskVal ///< Mask value
                                   );

/// Apply a shutter correction
///
/// Given a shutter correction (with dT for each pixel), applies this correction to an input image.
bool pmShutterCorrectionApply(pmReadout *readout, ///< Readout to which to apply shutter correction
                              const pmReadout *shutter ///< Shutter correction readout, with dT for each pixel
                             );

/// @}
#endif

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