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diff --git a/noao/imred/dtoi/doc/dtoi.ms b/noao/imred/dtoi/doc/dtoi.ms new file mode 100644 index 00000000..4f999259 --- /dev/null +++ b/noao/imred/dtoi/doc/dtoi.ms @@ -0,0 +1,576 @@ +.RP +.TL +An Overview of the IRAF DTOI Package +.AU +Suzanne Hammond Jacoby +.AI +IRAF Group - Central Computer Services +.K2 "" "" "*" +February 1987 +.br +Revised July 1988 + +.AB +This document describes the DTOI package, which contains tasks +for determining and applying a density to intensity transformation to +photographic data. The transformation is determined from a set +of calibration spots with known relative intensities. A curve is +interactively fit to the densities and intensities of the calibration +spots. The transformation is then applied and a new output image written. +.AE + +.NH +Introduction +.PP +The DTOI package contains tasks for computing and applying a density +to intensity transformation to photographic data. These tasks perform the +standard steps in linearizing data: calculating HD data points from +calibration spots, fitting a curve to these points and applying the HD +curve to the data. It is also possible to combine related HD curves. +Communication between the tasks is via text files which the user can +inspect or modify. It is intended +to be easy for users to introduce data from outside the DTOI package +into the processing. +.PP +There are currently six tasks in the package. They are: + +.ce +The \fBDTOI\fR Package +.TS +center; +n. +spotlist \&- Calculate densities and weights of calibration spots. +dematch \&- Match densities to log exposure values. +hdfit \&- Fit characteristic curve to density, exposure data. +hdtoi \&- Apply HD transformation to image data. +hdshift \&- Align related characteristic curves. +selftest \&- Test transformation algorithm. +.TE +.PP +The DTOI package does not currently support the self calibration of images, +but the addition of this capability is planned. This would involve +determining the HD curve from the data itself, by assuming the point spread +function scales linearly with intensity. +.PP +Upon entering the package, your calibration spots and images to be +transformed should be on the disk in IRAF image format. + +.NH +Determining the HD Curve Data +.PP +To determine the HD curve, you need two sets of data: the +measured photographic densities of a set of calibration spots and +the log exposure values corresponding to these measurements. The +log exposure values must be known a priori. Tasks \fIspotlist\fR and +\fIdematch\fR are used to assemble these two data sets. +.NH 2 +SPOTLIST +.PP +The first step is to calculate the density of +the calibration spots, each of which is a separate IRAF image or image +section. The spot density is either the median of the spot pixels or +the mean of the pixels when pixels more then a user specified number of +standard deviations away from the mean have been rejected. The numbers +in the spot image must be scaled to density; parameter \fBspotlist.scale\fR +is used such that density = input_value * scale. Task \fIspotlist\fR also +calculates the standard deviation of each spot and reports +the number of good pixels, i.e., the number of pixels not rejected +when determining the mean density. +The final product of this task is a record in the data base containing a +density for each spot. The scale factor used is also written to the data +base; it will be read later in task \fIhdtoi\fR. +.NH 2 +DEMATCH +.PP +Log exposure values must be matched to the measured density values. These +log exposure values must be known a priori and will be read from a file. +Task \fIdematch\fR retrieves the proper exposure information by +matching the wedge number, emulsion type and filter used. Once a match +has been made, the proper log exposure values are written to a record +in the database. +.PP +A database of log exposure values for the NOAO standard wedges is maintained +in a system file; the wedge/emulsion/filter combinations available are listed +in last section of this document. This file can be replaced with one specific +to any institution; the file name is supplied to task \fIdematch\fR as a +parameter. In this way the wedge file can be personalized to any application +and not be lost when the system is updated. + +.NH +Fitting the Curve +.PP +The HD curve, or characteristic curve, is a plot of density versus log +exposure. This curve is determined from the data points generated by +tasks \fIspotlist\fR and \fIdematch\fR. The objective is to fit +a curve to these points, such that Log exposure = F(Density). The +technique available in this package allows the independent variable of the +fit to be a transformation of the density (log opacitance, for example). +The log exposure and density values are +read from the database. If multiple entries for a particular record are +present in the database, the last one is used. +.NH 2 +HDFIT +.PP +Task \fIhdfit\fR fits a characteristic curve to density and log exposure +values in preparation for transforming an image from density to intensity. +Five functional forms of the curve are available: +.nf + + Power Series + Linear Spline + Cubic Spline + Legendre Polynomials + Chebyshev Polynomials + +.fi +.LP +It is possible to apply a transformation to the +independent variable (density above fog) prior to the fit. The traditional +choice is to fit log exposure +as a function of the log opacitance, rather than density directly. This is +sometimes referred to as the Baker, or Seidel, function. Transforming +the density has the effect of stretching the low density data points, which +tend to be relatively oversampled. +In the DTOI package, four independendent variables are currently available: +.nf + + Density + Log Opacitance + K50 - (Kaiser* Transform with alpha = 0.50) + K75 - (Kaiser* Transform with alpha = 0.75) + +.fi +.FS +* Margoshes and Rasberry, Spectrochimica Acta, Vol 24B, p497, (1969) +.FE +Any combination of transformation type and fitting function can be used and +changed interactively. Two combinations of interest are discussed here. + +The default fit is a power series fit where the independent variable is +Log Opacitance. That is: +.LP +.EQ + + "Log Exposure = " sum from k=0 to {ncoeff - 1} {A sub k Y sup k} + +.EN +.sp 1 +.EQ + "where Y = Log Opacitance = "Log sub 10 (10 sup Density - 1) +.EN +.LP +A fit that is expected to best model a IIIA-J emulsion is a power series +fit to a K75 transform of the density. That is, +.LP +.EQ + + "Log Exposure = "sum from k=0 to {ncoeff - 1} {A sub k Y sup k} + +.EN +.sp 1 +.EQ +"where Y = K75 transform = Density + 0.75 " Log sub 10 (1 - 10 sup -Density ) +.EN +.LP +Over the expected small dynamic range in variables of the fit, legendre +and chebyshev functions offer no advantages over a simple power series +functional form. The cubic and linear spline fits may follow the data very +closely, but with typically sparse data sets this is not desirable. It +is expected that power series fit will serve satisfactorily in all cases. + +.NH 3 +Interactive Curve Fitting +.PP +Task \fIhdfit\fR can be run interactively or not. In interactive mode, +points in the sample can be edited, added or deleted. Weighting values +can be changed as well as the fog value, the type of transformation +and the fitting function chosen. To obtain the best fit possible, interactive +fitting is recommended. A complete list of the available commands +is printed here; this list is also available interactively with the +keystroke '\fL?\fR'. +.TS +center; +c s s w(3.0i) +c l s. + + DTOI INTERACTIVE CURVE FITTING OPTIONS + +\fL?\fR Print options +\fLa\fR Add the point at the cursor position to the sample +\fLc\fR Print the coordinates and fit of point nearest the cursor +\fLd\fR Delete data point nearest the cursor +\fLf\fR Fit the data and redraw or overplot +\fLg\fR T{ +Redefine graph keys. Any of the following data types may be along +either axis: +T} +.T& +l l l. + \fLx\fR Independent variable \fLy\fR Dependent variable + \fLf\fR Fitted value \fLr\fR Residual (y - f) + \fLd\fR Ratio (y / f) \fLn\fR Nonlinear part of y + \fLu\fR Density above fog + +Graph keys: +.T& +c l s. + +\fLh\fR h = (x,y) transformed density vs. log exposure +\fLi\fR i = (y,x) log exposure vs. transformed density +\fLj\fR j = (x,r) transformed density vs. residuals +\fLk\fR k = (x,d) transformed density vs. the y(data)/y(fit) ratio +\fLl\fR l = (y,u) log exposure vs. density above fog (HD Curve) + +\fLo\fR Overplot the next graph +\fLq\fR T{ +Terminate the interactive curve fitting, updating the database file. +T} +\fLr\fR Redraw graph +\fLu\fR Undelete the deleted point nearest the cursor +\fLw\fR Set the graph window. For help type 'w' followed by '?'. +\fLx\fR Change the x value of the point nearest the cursor +\fLy\fR Change the y value of the point nearest the cursor +\fLz\fR Change the weight of the point nearest the cursor + +.T& +l s s w(3.0i). +T{ +The parameters are listed or set with the following commands which may be +abbreviated. To list the value of a parameter type the command alone. +T} + +.T& +l l s. + +\fL:show \fR[\fIfile\fR] Show the values of all the parameters +\fL:vshow \fR[\fIfile\fR] Show the values of all the parameters verbosely +\fL:errors \fR[\fIfile\fR] Print the errors of the fit (default STDOUT) +\fL:reset \fR T{ +Return to original conditions of x, y, wts and npts. +T} +\fL:ebars \fR[\fIerrors/weights\fR] T{ +The size of marker type '[hv]ebars' can show either standard deviations or +relative weights. +T} +\fL:function \fR[\fIvalue\fR] T{ +Fitting function (power, chebyshev, legendre, spline3, or spline1) +T} +\fL:transform \fR[\fIvalue\fR] Set the transform type (none, logo, k50, k75) +\fL:fog \fR[\fIvalue\fR] Change the fog level (or ":fog reset") +\fL:order \fR[\fIvalue\fR] Fitting function order +\fL:quit \fR Terminate HDFIT without updating database +\fL:/mark \fRstring T{ +Mark type (point, box, plus, cross, diamond, hline, vline, hebar, vebar, circle) +T} + +.T& +l s s. +T{ +Additional commands are available for setting graph formats and manipulating +the graphics. Use the following commands for help. +T} + +.T& +l l s. +\fL:/help\fR Print help for graph formatting option +\fL:.help\fR Print cursor mode help + +.TE +.PP +The value of fog can be changed interactively if you have +reason to override the value written in the database by \fIspotlist\fR. +You can reset the fog to its original value with the command ":fog reset". +A common problem with defining the HD curve is that some of +the calibration spot densities fall below fog. This is caused by either +the low signal to noise at low densities or by making a poor choice of +where to scan the fog level. These points are rejected from the fit +when a transformation of the density is being made, as the transform cannot +be evaluated for negative density. If the fog value or transformation +type is interactively changed so this problem no longer exists, +the spot densities are restored in the sample. + +The parameters of the final fit are written to a database which then +contains the information +necessary to reinitialize the curfit package for applying the transformation +in \fIhdtoi\fR. + +.NH +Applying the Transform +.PP +.NH 2 +HDTOI +.PP +Once the HD curve has been defined, it is applied to a density image +in task \fIhdtoi\fR. +Here the transformation is applied, as described by the fit parameters +stored in the database. If more than one record of fit parameters is +present, the last one is used. This means task \fIhdfit\fR can be +repeated until an acceptable solution is found; the last solution will +be used by \fIhdtoi\fR. On output, a new output image is written; the +input image is left intact. +.PP +The transformation is accomplished by using a look-up table. All possible +input values, from the minimum to maximum values found in the image, are +converted to density using the scale value read from the database, and then +to intensity using the fit parameters determined by \fIhdfit\fR. The input +value is then the index into the intensity table: +intensity = look_up_table (input_value). +.PP +A scaling factor can be applied to the final intensities, as typically +they will be < 1.0. (The maximum log exposure in the NOAO wedge database +is 0.0) By default, a saturated density pixel will be assigned the "ceiling" +intensity of 30000 and the other pixels are scaled accordingly. +The user is responsible for choosing a ceiling value +that will avoid having significant digits truncated. +The precision +of the transform is unaffected by scaling the +final intensities, although caution must be used if the output image +pixel type is an integer. +.PP +The value of fog to be used is entered by the user, and can be either +a number or a list of file names from which to calculate the fog value. +The fog value is subtracted from the input image before the transformation +takes place. +Again, consider density values below fog. Two choices are available for +these densities: the calculated intensity can be equal to the constant +value 0.0 or equal -1.0 times the intensity determined for absolute (density). + +.NH +Aligning Related HD curves +.PP +Calibration data sets from several plates can be combined once a shift +particular to each set has been removed. "Different spot exposures +define a series of HD curves which are parallel but mutually separated +by arbitrary shifts in log exposure, produced by differing lamp intensities +or exposure times. Generally, Kodak spectroscopic plates can be +averaged if [1] they come from the same emulsion batch and box, [2] +they receive identical hypersensitizing, [3] they are exposed similarly and +[4] they receive the same development." * +.FS +* "Averaging Photographic Characteristic Curves", John Kormendy, from +"ESO Workshop on Two Dimensional Photometry", Edited by P. Crane and +K.Kjar, p 69, (1980), an ESO Publication. +.FE +.NH 2 +HDSHIFT +.PP +Procedure \fIhdshift\fR calculates and subtracts a zero point shift to +bring several related HD curves into alignment. The individual shifts +are calculated by elimination of the first coefficient (Bevington, eqn 9-3): +.EQ + +a0 = y bar - a sub 1 X bar - a sub 2 X bar sup 2 - ~ ...~ - a sub n X bar sup n + +.EN +Here, the averages over y and X refer to individual calibration set averages; +the coefficients a1, ... an were previously calculated using data from all +calibration sets with task \fIhdfit\fR, and stored in the database. The +a0 term is calculated individually for each database; this term represents +the zero point shift in log exposure and will be different for each database. + +On output, the log exposure values in each database have been +shifted to the zero point shift of the first database in the list. The +log exposure records are now aligned and it would be appropriate +to run \fIhdfit\fR on the modified database list. +.NH +Testing the Transformation Algorithm +.PP +A test task is included to see if any numerical errors were introduced +during the density to intensity transformation. It also evaluates +truncation errors produced when an output image with integer pixels, +rather than reals, is written. +.NH 2 +SELFTEST +.PP +An intensity vector is generated from a density vector in two different +ways. The first method uses the density vector and known coefficients +to compute the intensity. The second method uses the curfit package +to generate a look up table of intensities as done in task \fIhdtoi\fR. The +residual of the two vectors is plotted; ideally the difference between +the 'known' and 'calculated' intensity is zero. +.PP +Task \fIselftest\fR also plots intensity as a function of density for +both integer and real output pixels. The user should investigate the +plot with the cursor zoom and expand capabilities to determine if +truncation errors are significant. +.NH +The Wedgefile Database +.PP +Task \fIdematch\fR reads a database and retrieves log exposure information +for certain combinations of wedge number, photographic emulsion and filter. +Those combinations included in the NOAO database are listed in the next +section, although any calibration data can be included if the values are +known. To modify the database, it is recommended that +you generate a new file rather than add records to the existing file. This +way, the modifications will not be lost when a new version of the IRAF +system is released. + +In the database, the information for each wedge makes up a separate record; +each record starts with the word \fBbegin\fR. Each record has a title field +and can have multiple emulsion/filter fields. The number of log exposure +values must be given, followed by the values written 8 per line. The order +of the exposure data can be either monotonically increasing or decreasing. +Here is an example: +.DS +begin 115 + title MAYALL 4-M PF BEFORE 15APR74 (CHROME) [MP1-MP968] + IIIAJ/UG2 16 + 0.000 -0.160 -0.419 -0.671 -0.872 -1.153 -1.471 -1.765 + -2.106 -2.342 -2.614 -2.876 -3.183 -3.555 -3.911 -4.058 + IIAO/UG2 16 + 0.000 -0.160 -0.418 -0.670 -0.871 -1.152 -1.468 -1.761 + -2.102 -2.338 -2.609 -2.870 -3.176 -3.547 -3.901 -4.047 + +.DE +.NH 2 +Contents of the NOAO Wedgefile +.LP +The following table lists the wedge/emulsion/filter combinations available in +the NOAO wedgefile database. +.TS +center; +l l s s s +l l l l l. + +\fBWedge 24 CTIO SCHMIDT WESTON TUBE SENSITOMETER. \fR + MONO/MONO + +.T& +l l s s s +l l l l l. +\fBWedge 48 PALOMAR 48-INCH SCHMIDT STEP WEDGE. \fR + MONO/MONO + +.T& +l l s s s +l l l l l. +\fBWedge 84 OLD 84-INCH SPOT SENSITOMETER (1967) \fR + MONO/MONO + +.TE +.TS +l l s s s +l l l l l. +\fBWedge 101 SPOT BOX 4, KEPT IN SCHOENING-S LAB. \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4760 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 115 MAYALL 4-M PF BEFORE 15APR74 (CHROME) [MP1-MP968] \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4770 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 117 CTIO 4-METER P.F. \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4770 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 118 CTIO 4-METER CASSEGRAIN \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4760 MONO/5200 MONO/5876 + MONO/6470 MONO/6900 + +.T& +l l s s s +l l l l l. +\fBWedge 119 SPOT BOX 5, KEPT AT MAYALL 4-METER. \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4760 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 120 SPOT BOX 6, KEPT AT 2.1-METER. \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4760 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 121 SPOT BOX 8, KEPT IN SCHOENING'S LAB. \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4760 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 122 SPOT BOX 7, AVAILABLE AT KPNO NIGHT ASST'S OFFICE \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4760 MONO/5200 MONO/5876 + MONO/6470C +.TE +.TS +l l s s s +l l l l l. +\fBWedge 123 MAYALL 4-M P.F. 15APR74 TO 21MAY74 [MP969-MP1051] \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4770 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 129 MAYALL 4-METER P.F. AFTER 21MAY74 [MP1052--> ] \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4760 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 130 MAYALL 4-METER CASS CAMERA. \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4760 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 138 TRAVELLING BOX AFTER 06JAN78. \fR + IIIAJ/UG2 IIAO/UG2 IIIAJ/*5113 IIAO/*5113 + IIAO/GG385 IIIAJ/CLEAR IIIAJ/GG385 IIAD/GG495 + 127/GG495 098/RG610 127/RG610 IVN/RG695 + MONO/4363 MONO/4770 MONO/5200 MONO/5876 + MONO/6470 + +.T& +l l s s s +l l l l l. +\fBWedge 201 TEN UCLA SPOTS (H. FORD, 10JAN78) \fR + MONO/MONO +.TE |