mdiscal

Messenger images are corrected for the following, in order, during calibration:

• Dark Current
• Linearity
• Smear
• Uniformity (flat field)
• Absolute coefficient

Dark current correction:

• None
No dark current correction is performed.
• Standard
Messenger images have a strip of dark current data on the left-hand side. This will take a median of the first three sample colums (for unbinned data) and use that for the dark current on a line by line basis.
• Linear
This will fit a line across the first column of data, which is dark current data, and use the line to determine the dark current correction.
• Model
There are independent dark models, developed on-ground. This will use the most recent of these models to correct the dark current.

Linearity Correction:
Linearity is the measure of how variable is each camera's DN level per unit exposure time and radiance, as a function of variation in exposure time or radiance. Using dark-corrected, desmeared DN values (DCDSI) taken from the center quarter of the images, response linearity was measured with both the NAC and WAC binned and not-binned.

Smear Correction:
Frame transfer smear corrections for MDIS follow the technique described for NEAR MSI image by Murchie et al. (1999). In brief, an image is exposed for a nominal integration time and is then transferred in 3.84 ms to a memory zone on the CCD, from which the analog signal is digitized line-by-line. Accumulation of signal continues during the finite duration of frame transfer, inducing a streak or frame-transfer smear in the wake of an illuminated object in the field of view, parallel to the direction of frame transfer. Note that the frame transfer occurs in the calibration pixels as well as on the imaging pixels. mdiscal accounts for the frame transfer smear contributed from the 16 calibration lines (removed from the PDS-archived images).

Uniformity Correction:
Response uniformity, or flat field, is a measure of pixel-to-pixel variations in responsivity. Measurements of response uniformity of the WAC and NAC were conducted in the OCF, at room temperature and while cold, by imaging the integrating sphere with the two 45W bulbs illuminating the interior.

Absolute Coefficient Correction:
This converts the DN values from responsivity to radiance values.

The MODEL dark current option cannot be used if the exposure time exceeds 1 second. In this case, the LINEAR model is selected and a message is issued to the user.

Note that there are some extreme cases where an image could not be radiometrically calibrated. When there is more than two factors of binning, FPU or PIXEL, then there are no valid dark pixel colums. For this case, calibrations using STANDARD or LINEAR cannot be used, however, the MODEL can. But, the MODEL cannot be used if the exposure time is exceeds 1 seconds. And in this case, the image cannot be calibrated. When these conditions are detected, a message is issued, but calibration continues using either the MODEL or NONE as the calibration mode.

The following is an excerpt from the MESSENGER MDIS calibration document on this process

        USAGE
        =====

        Raw units are of DN converted to the physical units
        of radiance or I/F, following the calibration equation:

        L(x,y,f,T,t,b) = Lin[DN(x,y,f,T,t,b,MET) - Dk(x,y,T,t,b,MET) - 
        Sm(x,y,t,b)] / {Flat(x,y,f,b) * t * [Resp(f,b,T)/Correct(f,MET)]}

        where:

        L(x,y,f,T,t,b) is radiance in units of W / (m**-2 microns**-1 sr**-1),
        measured by the pixel in column x, row y, through filter f, at CCD
        temperature T and exposure time t, for binning mode b,

        DN(x,y,f,T,t,b,MET) is the raw DN measured by the pixel in column x, row
        y, through filter f, at CCD temperature T and exposure time t, for binning
        mode b, and Mission Elapsed Time (MET),

        Dk(x,y,T,t,b,MET) is the dark level in a given pixel, derived from
        a model based on exposure time and CCD temperature,

        Sm(x,y,t,b) is the scene-dependent frame transfer smear for the pixel,

        Lin is a function that corrects small nonlinearity of detector response,

        Flat(x,y,f,b) is the non-uniformity or 'flat-field' correction,

        Resp(f,b,T) is the responsivity, relating dark-, flat-, and
        smear-corrected DN per unit exposure time to radiance,

        Correct(f,MET) is a time-variable correction to responsivity
        describing a sudden decrease in transmission of the WAC optics
        on 24 May 2011 and subsequent recovery to normal values, 
        interpreted as due to contamination associated with MESSENGER's
        first periapse season over Mercury's hot pole and the subsequent
        bake-off of the contaminant, 

        and

        t is the exposure time.

        The above equation assumes that data are in the native 12-bit format in
        which they were read off the CCD, and that onboard application of 12-to-8
        bit lookup tables (LUTs) has been inverted.

        This correction is done step-wise using the calibration tables and
        images in this directory as follows.


        (1) Inversion of 12 to 8 bit Compression
        ========================================

        8-to-12 bit inversion of DN values is required when the value of
        MESS:COMP12_8 is 1 (when the data are 8-bit). There are 8 inverse lookup
        tables (LUTs). The table to use is indicated by the value of MESS:COMP_ALG
        from 0 through 7. An 8-bit value (in a row of the table) is inverted by
        replacing it with the 12-bit value in the column corresponding to a
        particular LUT.

        The inversion tables are given in the product MDISLUTINV_0.


        (2) Subtraction of modeled dark level
        =====================================

        Two methods are used for subtraction of the dark level, one for 
        exposure times greater than 1 sec and one for exposure times less than 1 sec.

        In the method for exposure times less than 1 sec, the DN values are valid
        columns in the masked 'dark strip' at the edge of the CCD are fitted
        linearly as a function of line in the image. Then the fits are subtracted
        from the pixels in each line of the CCD.

        In the method for exposure times greater than 1 sec, a model is used which accounts
        for variations in column (sample) in the image, which the previous 
        method cannot do. However if the model were applied to longer exposures,
        it would yield larger residuals than the previous method.

        There are four separate models of dark level (dark current plus
        electronics bias), for the MDIS-WAC and MDIS-NAC (as indicated by the
        keyword INSTRUMENT_ID), and for each camera, without pixel binning turned
        on (MESS:FPU_BIN = 0) or with pixel binning turned on (MESS:FPU_BIN = 1).
        The models estimates the dark level Dk(x,y,t,T) as a function of column
        position x, row position y, exposure time t in milliseconds (as indicated 
        by the keyword MESS:EXPOSURE or EXPOSURE_DURATION), and CCD temperature T 
        (as indicated by the keyword MESS:CCD_TEMP):

        Dk(x,y,t,T) = C(T) + D(T) + [E(T) + F(T) * t] * y + {O(T) + P(T) * t +
         [Q(T) + S(T) * t] * y} * x

        Variables C(T), D(T), E(T), F(T), O(T), P(T), Q(T), and S(T) are all
        third-order functions of CCD temperature, for example:

        C(T) = H0 + H1 * T + H2 * T**2 + H3 * T**3

        In all cases x or y is in the range 0-1023 for a not-binned image (as
        indicated by the keyword MESS:FPU_BIN = 0) or 0-511 for a binned image (as
        indicated by the keyword MESS:FPU_BIN = 1). t is in units of milliseconds,
        and T is in UNCALIBRATED raw counts of CCD temperature.

        For each pixel in column x and row y of an image, application of the
        correction is:

        DN_dark(x,y,t,T) = DN(x,y,t,T) - Dk(x,y,t,T)

        where

        DN(x,y,t,T) is DN in 12-bit format,

        Dk(x,y,t,T) is the predicted DN level from the dark modeldark model, and

        DN_dark(x,y,t,T) is dark-corrected DN.

        The eight sets of coefficients for the WAC not-binned, WAC binned, NAC
        not-binned, and NAC binned dark models are given in the products
        MDISWAC_NOTBIN_DARKMODEL_0, MDISWAC_BINNED_DARKMODEL_0,
        MDISNAC_NOTBIN_DARKMODEL_0, and MDISNAC_BINNED_DARKMODEL_0 respectively.

        (3) Frame Transfer Smear Correction
        ===================================

        Accumulation of signal continues during the finite duration
        of frame transfer induces a streak or frame-transfer smear in the wake
        of an illuminated object in the field of view, parallel to the direction
        of frame transfer. This smear is approximated as:

        Sm(x,y,t,b,f) = SUMM(1,y-1) { t2/t * [DN_dark(x,y,t,b) -
        Sm(x,y,t,b,f)] / Flat(x,y,b,f)}

        where

        Sm(x,y,t,b,f) is the smear in column x and row y at exposure time t
        in binning mode b and filter f,

        Dk_dark (x,y,t,b) is dark-corrected DN in column x and row y at
        exposure time t and temperature T in binning mode b,

        Flat(x,y,b,f) is the flat-field correction in column x and row y in
        binning mode b and filter f,

        t is exposure time in milliseconds, and

        t2 is the time for frame transfer (about 3.4 ms) divided by the number of
        lines in the image in the direction of frame transfer, 1024 for
        full-frame images (when MESS:FPU_BIN = 0) or 512 for binned images (when
        MESS:FPU_BIN = 1).

        For each pixel in column x and row y of an image, application of the
        correction is :

        DN_dark_smear(x,y,t,b,f) = DN_dark(x,y,t,b,f) - Sm(x,y,t,b,f)

        where

        DN_dark_smear(x,y,t,b,f) is dark- and smear- corrected DN,

        DN_dark(x,y,t,b,f) is dark-corrected DN, and

        Sm(x,y,t,b,f) is the smear calculated as shown above.


        (4) Correction for CCD non-linearity
        ====================================

        To remove effects of nonlinearity in WAC image data, the following
        corrections should be applied after correction of dark current, bias,
        and smear.

        For DN_dark_smear > 1
        DN_lin = DN_dark_smear/[0.008760 * Ln(DN_dark_smear) + 0.936321]

        For DN_dark_smear less than or equal to 1
        DN_lin = DN_dark_smear/0.936321

        To remove effects of nonlinearity in NAC image data, the following
        procedure should be applied after correction of dark current, bias,
        and smear.

        For DN_dark_smear > 1
        DN_lin = DN_dark_smear/[0.011844 * Ln(DN_dark_smear) + 0.912031]

        For DN_dark_smear less than or equal to 1
        DN_lin = DN_dark_smear/0.912031

        where

        DN_dark_smear is the input dark- and smear-corrected DN, and

        DN_lin is linearized dark- and smear-corrected DN.


        (5) Flat-field correction
        =========================

        The flat field correction removes pixel to pixel differences in detector
        responsivity, so that the responsivity coefficients can be expressed as
        scalars for each filter. There is a separate flat-field image for MDIS-WAC
        and MDIS-NAC (as indicated by the keyword INSTRUMENT_ID), without pixel
        binning turned on (MESS:FPU_BIN = 0) or with pixel binning turned on
        (MESS:FPU_BIN = 1), for each separate filter (as indicated by the keyword
        FILTER_NUMBER). All of the files are in the 'FLAT' directory.

        For each pixel in column x and row y of an image, application of the
        correction is

        DN_flat(x,y,f,b) = DN_lin(x,y,f,b) / Flat(x,y,f,b)

        where

        DN_flat(x,y,f,b) is flat-fielded, linearized, dark- and smear-corrected
        DN,

        DN_lin(x,y,f,b) is linearized dark- and smear-corrected DN, and

        Flat(x,y,f,b) is the value in the appropriate flat-field image.


        (6) Conversion from DNs to radiance
        ===================================

        The value that relates corrected DN's measured per unit time to radiance
        is the responsivity. Responsivity is modeled as a function of which camera
        is being used (MDIS-WAC or MDIS-NAC as indicated by the keyword
        INSTRUMENT_ID), its binning state (as indicated by the keyword
        MESS:FPU_BIN), and in the case of the WAC the filter number (as indicated
        by the keyword FILTER_NUMBER). The coefficients used to calculate the
        responsivity are in the 'RESPONSIVITY' directory. For a camera, binning
        state, and filter, the responsivity is calculated from uncalibrated CCD
        temperature (as indicated by the keyword MESS:CCD_TEMP) as follows:

        Resp(f,T,b) = R(f,t=-30.3C,b) * [correction_offset(f,b) + T(CCD) * 
        correction_coef1(f,b) + T(CCD)^2 * correction_coef2(f,b)]

        where 

        Resp(f,T,b) is responsivity in filter f at CCD temperature T in binning 
        state b, 

        T(CCD) is raw CCD temperature in units of DNs, 

        R(f,t=-30.3C,b) is responsivity in filter f in binning state b at CCD 
        temperature of 1060 DN (-30.3C), 

        correction_offset(f,b) is camera- and filter-dependent temperature 
        correction offset for filter f and binning state b, 

        correction_coef1(f,b) is the camera- and filter-dependent temperature 
        correction first-order coefficient for filter f and binning state b.

        correction_coef2(f,b) is the camera- and filter-dependent temperature 
        correction second-order coefficient for filter f and binning state b.

        To apply responsivity to obtain radiance L, the expression is

        L(f) = DN_flat(f) / (t * Resp(f,T,b) * Correct(f, MET))

        where

        L is radiance in units of W / (m**2 microns**1 sr**1),

        DN_flat is dark-, smear-, linearity-, and flat field-corrected DN,

        t is the exposure time in seconds, 

        Resp(f,T,b) is the responsivity in filter f at CCD temperature T and
        binning state b, and 

        Correct(f, MET) is the temporal correction to responsivity for 
        filter f at time MET.


        (7) Conversion from radiance to I/F
        ===================================

        To convert from radiance to I/F (also known as radiance factor, the ratio
        of measured radiance to that which would be measured from a white
        perfectly Lambertian surface), the following expression should be applied:

        I_over_F(f) = L(f) * pi * (SOLAR_DISTANCE/149597870.691)**2 / F(f)

        where

        L(f) is calibrated radiance calculated as described above for some filter
        f,

        SOLAR_DISTANCE is that value for distance of the target object from the
        center of the sun in kilometers (as indicated by the keyword
        SOLAR_DISTANCE)

        149597870.691 is the number of kilometers in 1 AU

        F(f) is effective average solar irradiance sampled under the filter
        bandpass.

        The effective average solar radiance for each camera and bandpass is given
        in the SOLAR directory.
    

Additional corrective measures have been added to address a contamination event that occurred with the instruments on May 24, 2011 through January 3, 2012 after Mercury orbital insertion. The event and subsequent bake-off has been modeled as additional multiplicative component to the output values.

This example will show the calibration process of a MDIS image

mdiscal FROM=EW0089565626A.cub TO=EW0089565626A.calib.cub DARKCURRENT=MODEL

Calibrating EW0089565626A.cub

Calibrate an MDIS image The is the GUI for mdiscal when converting the uncalibrated cube EW0089565626A.cub to the calibrated cube EW0089565626A.calib.cub.

Input Image

Input Cube The is EW0089565626A.jpg before calibration

Output Image With Dark Model

Output With Dark Model The is the output generated by the default options