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pcintro noao.digiphot.photcal


I._INTRODUCTION · II._THE_CATALOG_AND_OBSERVATIONS_FILES_FORMAT
III._PREPARE_A_STANDARD_STAR_CATALOG_FILE · IV._PREPARE_A_STANDARD_STAR_OBSERVATIONS_FILE
V._PREPARE_THE_CONFIGURATION_FILE · VI._FITTING_THE_PARAMETERS_OF_THE_TRANSFORMATION_EQUATIONS
VII._APPLYING_THE_TRANSFORMATIONS_TO_THE_STANDARD_STARS · VIII._PREPARE_A_PROGRAM_STAR_OBSERVATIONS_FILE
IX._APPLYING_THE_TRANSFORMATIONS_TO_THE_PROGRAM_STARS

I. INTRODUCTION

The photometric calibration package PHOTCAL, contains a set of tasks for computing the transformation from the instrumental system to the standard photometric system, and applying the computed transformations to the observational data.

PHOTCAL distinguishes between two types of objects: standard stars , and program stars . Standard stars have known instrumental and standard photometric indices. Program stars have known instrumental photometric indices, but unknown standard photometric indices.

The standard indices of standard stars are contained in standard star catalogs known as catalog files . Each standard star catalog contains only a single entry for a given standard star. The instrumental indices of both standard and program stars are contained in observations catalogs, known as observations files . There may be any number of observations per star in an observations file.

PHOTCAL uses a setup file called the configuration file to specify the format of the input catalog and observations files and define the transformation equations to be fit.

Normally the user must perform the following logical steps to complete their photometric calibrations with PHOTCAL. However not all types of data require all the following steps.

[1]
Prepare a standard star catalog file using the MKCATALOG task.
[2]
Prepare a standard star observations file using the MKIMSETS and MKNOBSFILE tasks or alternatively the MKOBSFILE task.
[3]
Create the configuration file using the MKCONFIG and CHKCONFIG tasks.
[4]
Fit the transformation equations with the FITPARAMS task.
[5]
Apply the transformations to the standard star observations file using the EVALFIT or INVERTFIT tasks.
[6]
Prepare a program star observations file using the MKIMSETS and MKNOBSFILE tasks or alternatively the MKOBSFILE tasks.
[7]
Apply the transformations to the program star observations file using the EVALFIT or INVERTFIT tasks.

II. THE CATALOG AND OBSERVATIONS FILES FORMAT

PHOTCAL catalog and observation files are simple text files containing any number of columns. Columns are delimited by whitespace. The first column is always reserved for the star id or matching name, and the rest contain actual data such as positions, magnitudes, colors, errors, air mass, or any other quantity of interest. Comments can be inserted as separate lines at any point in the catalog or observations files by beginning the comment line with the character "#".

The star id is used to match observations with catalog entries, and to determine which objects are standard and which are program stars. Star ids may contain any non-blank characters, but lower case letters are converted to upper case, and characters not in the set [A-Z,0-9,+,-,_] are removed before star id matching. Catalog files must contain only a single entry per star. Observations files may contain multiple entries per star. Missing or unknown data values should be set to INDEF not left blank.

Normal catalog and observations files records are restricted in length to the maximum size of a text file line in IRAF, currently 161 characters including the newline. The maximum record length can be extended by replacing the the star id in column 1 with the continuation character "*".

Several preprocessors are provided to convert data coming from other IRAF packages, such as APPHOT and DAOPHOT, into a format suitable for PHOTCAL. If a preprocessor for a specific type of data does not exist, then the user will have to use other IRAF facilities to convert it to into the appropiate format, or write their own.

III. PREPARE A STANDARD STAR CATALOG FILE

A standard star catalog sutitable for input to PHOTCAL may be prepared in one of the following ways. The advantages and disadvantages of each method are briefly discussed.

[1]
Use one of the standard star catalogs supported by PHOTCAL and maintained in the directory "photcal$catalogs/". Each supported standard star catalog has an associated catalog format description file defining the format of the standard star catalog. The catalog format description file may be used as input to the MKCONFIG task. A list of currently supported standard star catalogs and their format files can be found in the file "photcal$catalogs/README".

The principal advantage of this option is that no data entry is required on the part of the user. The principal disadvantage is that PHOTCAL, in preparation for id matching, loads the entire standard star catalog into memory, even though the the number of observed standard stars may have been only a few dozen. For typical standard star catalogs containing a few hundred objects this is not a problem, but ver large standard star catalogs should be avoided.

[2]
Prepare a standard star catalog with the MKCATALOG task. MKCATALOG prompts the user for the catalog title, the id column name and width, and the names and widths of all the data columns. When column definition is complete, MKCATALOG writes the catalog definition information into the catalog header and the associated catalog format file and prompts for data. The catalog format description file created by MKCATALOG may be used as input to MKCONFIG. Type "help mkcatalog" for the details of task usage.

The principal advantages of using MKCATALOG are that the task always produces a PHOTCAL readable catalog and accompanying format description file, and that the standard star catalog contains values only for those objects that have actually been observed.

[3]
With a text file editor create or edit a standard star catalog which conforms to the requirements of PHOTCAL as described in the previous section.

The principal advantage of this option is that the user can take advantage of any spread sheet capabilities that his/her favorite editor has. The principal disadvantage is that a format description file is not automatically created along with the catalog.

[4]
Reformat an existing standard star catalog until it conforms to the requirements of photcal as described in the previous section. In some case this may require writing a local preprocessor program. PHOTCAL users should be aware of the PROTO package tasks JOIN and FIELDS, the LISTS package tasks COLUMN, and the UTILITIES package task TRANSLIT.

The first few lines of a representative catalog file produced by MKCATALOG are listed below. V, BV, and UB stand for the V magnitude, B-V color, and U-B color respectively. The non-blank lines beginning with # at the beginning of the file are for the internal use of the MKCATALOG task only, and are ignored by other PHOTCAL tasks.

# CATALOG: ubv.cat
# NCOLS: 7
# HDRLENGTH: 68
# 
# ID        V         error(V)  BV        error(BV) UB        error(UB)
# 8         8         8         8         8         8         8        

  105-307   12.050    0.020     0.690     0.020     0.220     0.020    
  105-405   8.309     0.004     1.521     0.001     1.905     0.007    
  105-411   10.620    0.014     0.950     0.010     0.620     0.008    
  105-256   11.820    0.013     0.610     0.012     0.180     0.022    

The accompanying format description file produced by MKCATALOG is listed below. This file associates a column number with the column name and can be used as input to MKCONFIG. The comments opposite the column definitions were not produced by MKCATALOG but typed in later.


# Declare the catalog variables

catalog

V          2		# the V magnitude
error(V)   3		# the error in the V magnitude
BV         4		# the B-V color
error(BV)  5		# the error in the B-V color
UB         6		# the U-B color
error(UB)  7		# the error in the U-B color

IV. PREPARE A STANDARD STAR OBSERVATIONS FILE

A standard star observations file suitable for input to PHOTCAL may be prepared in one of the following ways. APPHOT and DAOPHOT users should use options [1] or [2]. Other users must either enter their data by hand using options [3] and [4], or write a local program to prepare their data for input to PHOTCAL, option [5].

[1]
If the standard star magnitudes were computed with APPHOT or DAOPHOT and consist of many individual and repeated observations of standard star fields, then use MKIMSETS followed by MKNOBSFILE to create an observations file. MKIMSETS creates an image set definition file, telling MKNOBSFILE which images taken in which filters belong to the same observation of a given stellar field. For each observations file written, MKNOBSFILE creates an associated format description file defining the format of the new observations file and suitable for input to MKCONFIG. MKNOBSFILE is set up to run automatically once the image set file is defined. Type "help mknobsfile" for details.
[2]
If the standard star magnitudes in one or more colors were computed with APPHOT or DAOPHOT and all the standard stars are in one stellar field, use the MKOBSFILE task to create an observations file. For each observations file created, MKOBSFILE creates an associated format descriptin file defining the format of the new observations file, and suitable for input to MKCONFIG. MKOBSFILE prompts the user for all the required input. Type "help mkobsfile" for details.
[3]
Prepare a standard star observations file with the MKCATALOG task. MKCATALOG prompts the user for the observations file title, the id column name and width, and the names and widths of all the data columns. When column definition is complete, MKCATALOG writes the observations file definition information into the observations file header and the associated format description file and prompts for data. The format description file created by MKCATALOG may be used as input to MKCONFIG if the "catalog" keyword (see the example in the previous section) is changed to "observations". Type "help mkcatalog" for the details of task usage.
[4]
With the text editor create or edit a standard star observations file which conforms to the requirements of PHOTCAL as described in the previous section.
[5]
Write a local program to prepare the data for input to PHOTCAL.

A sample image set file produced by MKIMSETS is shown below. The labels STD1, STD2, ..., STD7 stand for standard star fields 1, 2, ..., 7 and the c0* labels are the names of images of each field taken through filters U, B, and V respectively.

    STD1 :  c023  c022  c021
    STD2 :  c024  c025  c026
    STD3 :  c029  c028  c027
    STD4 :  c033  c031  c032
    STD5 :  c061  c060  c059
    STD6 :  c064  c063  c062
    STD7 :  c069  c066  c065

The first few lines of the observations file produced by MKNOBSFILE using the above image set file both before and after the user has edited in the correct standard star ids is listed below. Note that there is usually more than 1 star in the field. In fact the data set above included 17 standard stars and 5 additional stars that the automatic star finding algorithm picked up. Note also that some known bad data points in the original observations file have been replaced with the undefined value INDEF.


before editing

# FIELD     FILTER OTIME    AIRMASS  XCENTER  YCENTER      MAG      MERR

STD1-1      1      INDEF      1.276   156.43   518.23   20.077     0.031 
*           2      INDEF      1.270   155.37   521.12   17.712     0.053 
*           3      INDEF      1.265   152.16   519.62   17.044     0.019 
STD1-2      1      INDEF      1.276   481.39   357.19   18.683     0.009 
*           2      INDEF      1.270   480.57   360.07   14.919     0.005 
*           3      INDEF      1.265   477.07   358.62   13.292     0.002 
STD1-3      1      INDEF      1.276   507.69   128.53   19.144     0.014 
*           2      INDEF      1.270   507.06   131.44   16.612     0.020 
*           3      INDEF      1.265   503.42   130.29   15.587     0.008 
STD2-1      1      INDEF      1.305   719.59   399.17   19.863     0.097 
*           2      INDEF      1.315   718.79   401.30   17.339     0.043 
*           3      INDEF      1.320   715.47   402.55   16.601     0.033 
STD2-2      1      INDEF      1.305   470.72   393.68   16.675     0.005 
*           2      INDEF      1.315   469.71   396.22   14.743     0.004 
*           3      INDEF      1.320   466.58   397.27   14.030     0.004 
STD2-3      1      INDEF      1.305   498.75   204.35   19.413     0.057 
*           2      INDEF      1.315   497.73   206.40   17.469     0.042 
*           3      INDEF      1.320   494.55   207.64   16.662     0.032 
STD2-4      1      INDEF      1.305   182.44   209.60   19.748     0.073 
*           2      INDEF      1.315   181.10   211.95   18.056     0.074 
*           3      INDEF      1.320   178.21   213.03   17.034     0.044 
STD3-1      1      INDEF      1.251   397.57   200.65   19.060     0.007 
*           2      INDEF      1.236   396.58   200.38   15.725     0.005 
*           3      INDEF      1.231   393.53   200.51   14.237     0.007 

after editing

# FIELD     FILTER OTIME    AIRMASS  XCENTER  YCENTER      MAG      MERR

STD1-1      1      INDEF      1.276   156.43   518.23   20.077     0.031 
*           2      INDEF      1.270   155.37   521.12   17.712     0.053 
*           3      INDEF      1.265   152.16   519.62   17.044     0.019 
105-405     1      INDEF      1.276   481.39   357.19   18.683     0.009 
*           2      INDEF      1.270   480.57   360.07   14.919     0.005 
*           3      INDEF      1.265   477.07   358.62   13.212     0.002 
105-411     1      INDEF      1.276   507.69   128.53   19.144     0.014 
*           2      INDEF      1.270   507.06   131.44   16.612     0.020 
*           3      INDEF      1.265   503.42   130.29   15.487     0.008 
STD2-1      1      INDEF      1.305   719.59   399.17   19.863     0.097 
*           2      INDEF      1.315   718.79   401.30   17.339     0.043 
*           3      INDEF      1.320   715.47   402.55   16.601     0.033 
105-257     1      INDEF      1.305   470.72   393.68   16.675     0.005 
*           2      INDEF      1.315   469.71   396.22   14.743     0.004 
*           3      INDEF      1.320   466.58   397.27   14.030     0.004 
105-262     1      INDEF      1.305   498.75   204.35   INDEF      0.057 
*           2      INDEF      1.315   497.73   206.40   17.469     0.042 
*           3      INDEF      1.320   494.55   207.64   INDEF      0.032 
STD2-4      1      INDEF      1.305   182.44   209.60   19.748     0.073 
*           2      INDEF      1.315   181.10   211.95   18.056     0.074 
*           3      INDEF      1.320   178.21   213.03   17.034     0.044 
106-575     1      INDEF      1.251   397.57   200.65   19.060     0.007 
*           2      INDEF      1.236   396.58   200.38   15.725     0.005 
*           3      INDEF      1.231   393.53   200.51   14.237     0.007 

The accompanying format description file produced by MKNOBSFILE is listed below. This file associated column numbers with column names. The filter numbers 1, 2, 3 were written into the image headers by the data taking program, and subsequently picked up by the APPHOT package tasks computed the magnitudes. They stand for filters U, B and V respectively.

# Declare the observations file variables

observations

T1            3              # time of observation in filter 1
X1            4              # airmass in filter 1
x1            5              # x coordinate in filter 1
y1            6              # y coordinate in filter 1
m1            7              # instrumental magnitude in filter 1
error(m1)     8              # magnitude error in filter 1

T2            10             # time of observation in filter 2
X2            11             # airmass in filter 2
x2            12             # x coordinate in filter 2
y2            13             # y coordinate in filter 2
m2            14             # instrumental magnitude in filter 2
error(m2)     15             # magnitude error in filter 2

T3            17             # time of observation in filter 3
X3            18             # airmass in filter 3
x3            19             # x coordinate in filter 3
y3            20             # y coordinate in filter 3
m3            21             # instrumental magnitude in filter 3
error(m3)     22             # magnitude error in filter 3

V. PREPARE THE CONFIGURATION FILE

The configuration file is a text file, created by the user, that specifies both the format of the input data and the form of the transformation equations. A detailed description of the grammar and syntax of the configuration file can be obtained by typing the following command.


ph> help config

The configuration file can be prepared in one of the following ways.

[1]
Run the MKCONFIG task using the output of MKCATALOG or direct terminal input to define the catalog file format, the output of the MKNOBSFILE or MKOBSFILE tasks or direct terminal input to define the observations file format, and one of the standard template transformation section files or direct terminal input to define the transformation equations. Users are urged to use MKCONFIG if they are new to PHOTCAL, if the catalog file is one of the supported catalogs, or if the observations file was made with one of the standard preprocessors MKNOBSFILE or MKOBSFILE.
[2]
Use the text editor to make small corrections to an existing functioning configuration file. This is the recommended method if the transformation equations have changed from a previous PHOTCAL reduction session but the format of the standard star and observations catalogs has not, or if the user has become familiar with the PHOTCAL configuration file format.
[3]
Use the text editor to create a configuration file from scratch.

The grammar and syntax of the configuration file can be checked with the CHKCONFIG task. If an error was found, the program will print the line and the word where the error was detected and the user must reedit the file until no errors are found.

A sample configuration file is shown below.


# Declare the catalog file variables

catalog

V               2
error(V)	3
BV              4
error(BV)	5
UB              6
error(UB)	7

# Declare the observations file variables

observations

T1            3              # time of observation in filter 1
X1            4              # airmass in filter 1
x1            5              # x coordinate in filter 1
y1            6              # y coordinate in filter 1
m1            7              # instrumental magnitude in filter 1
error(m1)     8              # magnitude error in filter 1

T2            10             # time of observation in filter 2
X2            11             # airmass in filter 2
x2            12             # x coordinate in filter 2
y2            13             # y coordinate in filter 2
m2            14             # instrumental magnitude in filter 2
error(m2)     15             # magnitude error in filter 2

T3            17             # time of observation in filter 3
X3            18             # airmass in filter 3
x3            19             # x coordinate in filter 3
y3            20             # y coordinate in filter 3
m3            21             # instrumental magnitude in filter 3
error(m3)     22             # magnitude error in filter 3


transformation

fit  u1 = 0.0, u2 = -.07, u3 = 0.70
UFIT : m1 = V + BV + UB + u1 + u2 * UB + u3 * X1

fit  b1 = 0.0, b2 = -.06, b3 = 0.30
BFIT : m2 = V + BV + b1 + b2 * BV + b3 * X2

fit  v1 = 0.0, v2 = 0.05, v3 = 0.20
VFIT : mv = V + v1 + v2 * BV + v3 * Xv

VI. FITTING THE PARAMETERS OF THE TRANSFORMATION EQUATIONS

The heart of the PHOTCAL package is the parameter fitting task FITPARAMS. A detailed description of this task and its parameters can be obtained by typing the following command.


ph> help fitparams

FITPARAMS takes the observation files, catalog files, and configuration file, and computes the value of the fit parameters for each of the transformation equations specified in the configuration file. Equations will be processed in the same order in which they occur in the configuration file. The output of FITPARAMS is a text database file containing one record, identified by the transformation equation label, for each equation fit. Successive fits are appended to the end of the database file. If more than one fit has the same label the last fit performed will be used by the evaluation tasks.

Only standard stars with known instrumental magnitudes and photometric indices are used to compute the parameters of each transformation equation. Standard stars are identified by matching the id in the observations catalog against the list of ids in the standard star catalog.

The fitting process can be either interactive or non-interactive. Interactive fitting is the default. In interactive mode, the user is presented with plots of the data and the fit, can reject points automatically using a k-sigma rejection algrotihm, delete points interactively with the cursor, change which parameters are to be fit and which are to be held constant, and so on. A detailed description of all the interactive options and colon commands can be obtained by typing the following command.


ph> help inlfit

The database file produced by FITPARAMS for the catalog and observations files listed in sections III and IV and configuration file listed in section V is shown below.

# Mon 10:41:04 06-May-91
begin	UFIT
	status	0	(Solution converged)
	variance	4.965303E-4
	stdeviation	0.02228296
	avsqerror	1.
	averror		1.
	avsqscatter	0.
	avscatter	0.
	chisqr		4.965303E-4
	msq		3.901309E-4
	rms		0.01975173
	reference	mu
	fitting		V+BV+UB+u1+u2*UB+u3*Xu
	weights		uniform
	parameters	3
		u1	(fit)
		u2	(fit)
		u3	(fit)
	derivatives	3
		0.1
		0.1
		0.1
	values	3
		6.108767
		-0.04842735
		0.7180178
	errors	3
		0.05704632
		0.008730207
		0.04209311

# Mon 10:41:14 06-May-91
begin	BFIT
	status	0	(Solution converged)
	variance	0.002550806
	stdeviation	0.0505055
	avsqerror	1.
	averror		1.
	avsqscatter	0.
	avscatter	0.
	chisqr		0.002550806
	msq		0.00207253
	rms		0.04552504
	reference	mb
	fitting		V+BV+b1+b2*BV+b3*Xb
	weights		uniform
	parameters	3
		b1	(fit)
		b2	(fit)
		b3	(fit)
	derivatives	3
		0.1
		0.1
		0.1
	values	3
		4.826268
		-0.08220235
		0.275757
	errors	3
		0.1189408
		0.02718129
		0.08517767

# Mon 10:41:21 06-May-91
begin	VFIT
	status	0	(Solution converged)
	variance	9.547584E-4
	stdeviation	0.03089917
	avsqerror	1.
	averror		1.
	avsqscatter	0.
	avscatter	0.
	chisqr		9.547584E-4
	msq		7.501673E-4
	rms		0.02738918
	reference	mv
	fitting		V+v1+v2*BV+v3*Xv
	weights		uniform
	parameters	3
		v1	(fit)
		v2	(fit)
		v3	(fit)
	derivatives	3
		0.1
		0.1 
		0.1 
	values	3
		4.632307
		0.02190715
		0.1877689
	errors	3
		0.07831987
		0.01721398
		0.0573602

VII. APPLYING THE TRANSFORMATIONS TO THE STANDARD STARS

This step is optional since the goodness of fit can be assessed more efficiently from within the FITPARAMS task. However in some cases the user may want a record of the fitted photometric indices for the standard stars and the residuals from the fit.

There are two tasks for evaluating the transformation equations and which one the user must select depends on how he/she has defined the transformations equations.

If all references to the catalog file variables are on the left-hand side of the transformation equations and the right-hand side is a function of the observations file variables only, then the user should use EVALFIT. The transformation equations used for reducing photoelectric photometry are often written in this manner.

If the left-hand side of the transformation equation is a function of the observations file variables and all references to the catalog files variables are on the right-hand side of the transformation equations then the user must use INVERTFIT. The transformation equations for reducing CCD photometry are usually written in this manner.

The full ouput of INVERTFIT for the partial catalog and observations files listed in section III and IV and the configuration file shown in section V are listed below. Only observations which were successively matched with objects in the standard star catalog files are shown. The fits for objects with undefined observational variables could not be successfully inverted producing a row of INDEF values.

# Tue 15:50:37 14-May-91
# List of observations files:
#		ubv.std
# Number of catalog files:
#		ubv.cat
# Config:	ubv.cfg
# Parameters:	ubv.fit
#
# Computed indices for standard objects only
#
# Columns: 
#	1	object id
#	2	V
#	3	error(V)
#	4	resid(V)
#	5	BV
#	6	error(BV)
#	7	resid(BV)
#	8	UB
#	9	error(UB)
#	10	resid(UB)


105-405  8.308  0.002 0.001  1.563  0.006  -0.042 1.878  0.011  0.027
105-411  10.597 0.008 0.023  0.913  0.024  0.037  0.639  0.027  -0.019
105-257  9.140  0.004 0.000  0.451  0.006  0.039  0.040  0.007  -0.020
105-262  INDEF  INDEF INDEF  INDEF  INDEF  INDEF  INDEF  INDEF  INDEF
106-575  9.345  0.007 -0.004 1.322  0.010  -0.014 1.457  0.009  0.026
106-728  INDEF  INDEF INDEF  INDEF  INDEF  INDEF  INDEF  INDEF  INDEF
107-998  10.399 0.010 0.041  0.602  0.018  0.028  0.217  0.020  -0.057
107-991  INDEF  INDEF INDEF  INDEF  INDEF  INDEF  INDEF  INDEF  INDEF
107-990  9.555  0.005 0.005  0.455  0.009  0.035  0.047  0.009  -0.047
114-473  8.514  0.004 0.006  1.005  0.007  0.005  0.832  0.008  -0.032
114-353  INDEF  INDEF INDEF  INDEF  INDEF  INDEF  INDEF  INDEF  INDEF
114-151  10.708 0.005 -0.048 0.748  0.011  0.002  0.221  0.014  0.069
114-236  10.446 0.005 0.034  0.687  0.010  -0.057 0.093  0.011  0.007
111-775  INDEF  INDEF INDEF  INDEF  INDEF  INDEF  INDEF  INDEF  INDEF
111-773  8.980  0.005 -0.017 0.270  0.006  -0.064 -0.258 0.005  0.047
111-1342 9.263  0.006 -0.043 1.702  0.009  -0.012 1.726  0.076  0.054
111-733  9.219  0.006 -0.039 0.262  0.007  0.038  0.172  0.007  0.008

VIII. PREPARE A PROGRAM STAR OBSERVATIONS FILE

A program star observations file is prepared in the identical manner to the standard star observations file as described in section IV. In fact there is no intrinsic reason why standard star and program star observations cannot occupy the same observations file since they can be separated later by the EVALFIT and INVERTFIT tasks. In the sample observations file shown in section IV objects with names like 105-411 are the actual standard stars and those with names like STD* can, for the purpose of illustration, be regarded as program stars.

IX. APPLYING THE TRANSFORMATIONS TO THE PROGRAM STARS

The transformation equations are applied to the program stars in the same way they are applied to the standard stars ad described in section VII.

The ouput of INVERTFIT for the partial catalog and observations files listed in section III and IV and the configuration file shown in section V are listed below. Only observations which were not successfully matched with objects in the standard star files are shown. Note that the residuals from the fit cannot be computed for program objects and are therefore not output.

# Tue 16:17:11 14-May-91
# List of observations files:
#		ubv.obs
# Number of catalog files:
#		ubv.cat
# Config:	ubv.cfg
# Parameters:	ubv.fit
#
# Computed indices for program objects only
#
# Columns: 
#	1	object id
#	2	V
#	3	error(V)
#	4	BV
#	5	error(BV)
#	6	UB
#	7	error(UB)


STD1-3  12.165  0.019  0.403  0.063  0.508   0.069
STD2-2  12.136  0.045  0.796  0.096  -0.242  0.115
STD2-4  11.710  0.034  0.479  0.061  0.660   0.113
STD6-3  10.589  0.006  0.619  0.016  -0.069  0.022
STD7-5  11.852  0.059  0.406  0.069  0.981   0.129

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