kai.mtf.mtf
Module Contents
Classes
Functions
|
image - 2D numpy array containing the image. Image must be square. |
|
Make a 2D hanning kernel from the seperable 1D hanning kernels. The |
|
NAME: |
|
NAME: |
|
|
|
|
|
NAME: |
|
2D auto correlation. |
|
NAME: |
|
" |
|
NAME: |
|
NAME: |
|
NAME: |
|
NAME: |
|
NAME: |
|
|
|
" |
|
" |
|
" |
|
NAME: |
Attributes
- kai.mtf.mtf.get_mtf(image, params, sources)[source]
image - 2D numpy array containing the image. Image must be square. params - a dictionary with the various parameters used to calculate
the MTF.
- sources - (def=None) and optional 2D numpy array (same size as image)
that contains the distribution of stars in the image as delta functions.
- kai.mtf.mtf.hanning(xsize, ysize, invert=False)[source]
Make a 2D hanning kernel from the seperable 1D hanning kernels. The default kernel peaks at 1 at the center and falls to zero at the edges. Use invert=True to make an inner mask that is 0 at the center and rises to 1 at the edges.
- kai.mtf.mtf.mtffunc_keck(pp, nu=None, wave=None, F=None, D=None, Apix=None, pupil=None, tperf=None, sources=None, output='system', fjac=None)[source]
- NAME:
MTFFUNC_KECK
- PURPOSE:
Given the appropriate input parameters, returns the square of the 1-D Modulation Transfer Function (MTF)^2 of an optical system consisting of a telescope + detector + atmosphere + Adaptive Optics (AO) system.
- CATEGORY:
How should I know?
- CALLING SEQUENCE:
- RESULT=MTFFUNC_KECK(NU, PARAMS, [/PERF, /ATMOS_AO, $
SPDIST=SPDIST])
- INPUTS:
NU: The spatial frequencies at which the MTF will be computed, in normalized units (i.e. nu=1 at spatial frequency D/lambda for a circular aperture telescope), and need not be regularly gridded.
PARAMS: A structure of parameters defined as follows:
- params.lambda - wavelength in meters of the
observation
- params.f - effective focal length at detector
in meters
- params.D - telescope pupil diameter in meters,
defining the normalized spatial frequency NU which is in units of D/lambda; not necessarily 10 meters for Keck! (see PROCEDURE below)
- params.A - width of detector pixel in meters,
27 microns for the NIRC2 narrow field.
- params.pupil - a string equal to the name of
the pupil-stop of the NIRC2 camera (see documentation for T_PERFECT_KECK for a list of available pupil-stop names) or for a circular pupil, the scalar floating point value of the pupil’s central obscuration. The data type of this parameter deterimines the form of the pupil MTF used (see PROCEDURE below).
- params.L0 - the outer scale of turbluence, in
meters, for a modified Kolmogorov spectrum
- params.sigma - the width of the AO system
deformable mirror’s (DM’s) influence function as projected onto the pupil plane, in meters.
- params.w - scaling factor for the influence
function’s Fourier transform; mimics variable AO correction (see documentation for FT_INFL_FUNCTION)
params.delta - wavefront measurement error params.cmult - constant scaling factor of the output
MTF
- params.N - additive constant to output MTF
representing a noise floor
- params.r0 - wavelength specific Fried
parameter in meters (see PROCEDURE below).
- KEYWORD PARAMETERS:
- SPDIST: Set this keyword to a vector the same size as nu, the
1-D power spectrum of the source distribution power spectrum of an image for which you wish to fit an MTF. The output (MTF)^2 is multiplied by this vector before output.
- /PERF: If this keyword is set, RESULT is the square of the
diffraction limited pupil MTF.
- /ATMOS_AO: If this keyword is set, RESULT is the square of
the AO filtered atmospheric MTF.
- /PIX
Returns the MTF^2 of an ideal pixel.
- _EXTRA: Use this keyword to pass in a structure containing
constant parameters that need not be recomputed each time MTFFUNC_KECK is called. This is useful for speeding up an iterative fitting procedure that uses MTFFUNC_KECK. The structure passed in via this keyword must contain the following parameters/tags:
- _EXTRA = {lambda:lambda, f:f, D:D, pupil:pupil, $
A:A, TPERF:TPERF, SPDIST:SPDIST}
where lambda, f, D, A, and pupil are definted exactly as they are for input via PARAMS; TPERF is a vector of size equal to NU and is the diffraction limited pupil MTF (N.B., not the squared MTF) and is equivalent to the square root of the output of MTFFUNC_KECK with the /PERF keyword set; SPDIST is the power spectrum of and image’s source distribution function, identical to SPDIST.
If the keyword _EXTRA is set to this structure, then PARAMS must not be a structure containing all of the parameters defined in PARAMS above, but must be a 7 element vector defined as such:
- PARAMS[0] = L0, PARAMS[1] = sigma, PARAMS[2] = w,
- PARAMS[3] = delta, PARAMS[4] = cmult, PARAMS[5]= N,
PARAMS[6] = r0.
Setting the keyword SPDIST overrides the source distribution power spectrum passed in via the _EXTRA keyword. If the _EXTRA keyword is not set and a structure of parameters is passed in via PARAMS, then SPDIST is the only way to multiply the output of MTFFUNC_KECK by a vector before returning.
- OUTPUTS:
RESULT: The (MTF)^2, evaluated at the input spatial frequencies, NU.
- RESTRICTIONS:
NU must be greater than zero.
- PROCEDURE CALLS:
T_ATMOS_AO(), T_PIX(), T_PERFECT_KECK(), T_PERFECT()
- PROCEDURE:
If PARAMS.pupil is a string, it must specify the pupil stop name of the NIRC2 camera that was in place at the time of the observation. See the documentation for NIRC2PUPIL for a list of acceptable pupil stop names. In this case, the pupil MTF is numerically calculated as the autocorrelation function of the Keck pupil via the procedure T_PERFECT_KECK.
If PARAMS.pupil is a floating point scalar, the pupil MTF is calculated analytically via the procedure T_PERFECT for a circular pupil with central obscuration PARAMS.pupil. (See the documentation for T_PERFECT.) This functionality is not intended for use with Keck AO data, but is included in the event this software is applied to data from other AO systems, such as the Lick 3-meter telescope.
PARAMS.delta is untested, and for the time being should be left set to zero.
In general PARAMS.D should not be set to the familiar 10 meters, which is the effective diameter of the Keck pupil. Since this parameter defines the maximum spatial frequency D/lambda to which the telescope is sensitive, it should be equal to the diameter of the circle inscribing the Keck pupil. This is because the lambda/D minimum angle changes depending on orientation in the image plane, and in certain orientations the diameter appropriate for this specification is D = 10.99 m.
r0 is the wavelength specific Fried parameter. Generally, the r0 specifying seeing conditions is quoted for a wavelength of 500 nm. If one has reason to believe that the r0 for a set of observations is 20 cm, then the wavelength specific r0 is given as
r0_lambda = r0 * (lambda/500 nm)^(6/5)
and this is the r0 that should be specified in PARAMS.RO.
The effective focal length at the detector, PARAMS.F, is related to the platescale of the detector by
F = Apix / platescale
where platescale is in radians / pixel. If the platescale and the pixel size is accurately known, F should be calculated in this manner.
- EXAMPLE:
Generate a model MTF for an H-band NIRC2 image at the .01 arcsec/pixel platescale at normalized spatial fequencies in the image plane from 0 to 1:
- params={lambda:1.6e-6, F:557.0, D:10.99, $
L0:30.0, sigma:0.56, w:1.5, delta:0.0, cmult:1.0, $ N:1e-4, r0:0.65, Apix:27e-6, pupil:’largehex’}
nu = findgen(100)/99. tsys_squared = mtffunc_keck(nu,params)
- MODIFICATION HISTORY:
Written by: Christopher D. Sheehy, January 2006.
- kai.mtf.mtf.fitmtf_keck(nu, power, error, pspec_sources, clip=None, startParams=None, relStep=0.2, quiet=False)[source]
- NAME:
FITMTF_KECK
- PURPOSE:
Uses MPFIT to perform a constrained Levenberg-Markwardt fit of a model MTF to data from a Keck adaptive optics image. It is highly recommended that the user edit this procedure to suit his or her particular needs, i.e. changing the default initial guesses for the fit parameters and the step size to MPFIT.
This procedure is meant as a guide to illustrate how to use MPFIT in conjunction with the AO MTF software. Just because MPFIT returns best fit parameters does not mean that it has found an absolute minimum in Chi-squared. As with most non-linear fit routines, some tinkering may be required to avoid local minima and to obtain accurate fits. In other words, this procedure should not be applied blindly.
In general, a good way to obtain accurate fits is to first perform the fits with decent starting guesses for the fit parameters and specifying a relatively large step size over which MPFIT calculates the numerical derivative of the fit function w.r.t. the fit parameters. Once the best fit parameters are obtained from this iteration, the step size can be decreased and the best fit parameters from the first iteration should be used as the starting guesses for the parameters in the second iteration.
A good rule of thumb that seems to work in some (many?) cases is specifying the step size in the first iteration to be 20% of the parameters’ respective values, and a step size of 2% in the second interation. This can be accomplished by changing the values of PARINFO[*].relstep from 0.20 to 0.02 within the procedure or via the RELSTEP keyword defined at the main level. Different step sizes for different parameters can be specified by editing PARINFO[*].relstep within the procedure.
- CATEGORY:
???
- CALLING SEQUENCE:
- FITMTF_KECK, filename, params, perror, covar, chisq, $
[start=start, relstep=relstep, quiet=quiet]
- INPUTS:
- FILENAME: A scalar string specifying the filename of an IDL
save file containing the data to which the model MTF is fit. The command
restore, FILENAME
must restore the variables NU, POWER, ERROR, and SPDIST, which are vectors of equal size. These variables are the outputs of the routine GETMTF.
- KEYWORD PARAMETERS:
- START: Set this keyword equal to a structure containing
starting guesses for the fit parameters as defined in the documentation for MTFFUNC_KECK. If not set, they the default values must be defined within the procedure.
- CLIP: Set this keyword equal to a scalar value defining the
normalized spatial frequency (defined by NU) below which the data restored from FILENAME will be ignored. By default, this value is None (no clipping). Setting CLIP = 0.0 fits all of the data. However, this is generally not recommended because imperfect sky subtraction of the image from which NU and POWER were computed usually contaminates the power spectrum at low spatial frequencies. The recommended value is 0.02.
- RELSTEP: Defines the relative step size over which MPFIT
computes the numerical derivative of Chi-sqared w.r.t. the fit parameters. Sets the value PARINFO[*].relstep, which is an input to MPFIT (see the documentation for MPFIT).
- /QUIETSet this keyword to supress the printed output of
MPFIT. Generally, though, it is good practice to keep tabs on what MPFIT is doing as it’s proceding with the fit.
- OUTPUTS:
- PARAMS: A structure of the best fit parameters as determined
by MPFIT; can be used as the input parameters to MTFFUNC_KECK, MTF2PSF, MTF2EE, or any of MTFFUNC_KECK’s subsidiary routines.
The parameters that are fit are L0, sigma, w, delta, cmult, N, and r0. The rest are only supplied as information to MTFFUNC_KECK. In addition, some of these fit parameters may be held constant if they are known or assumed (SIMGA and DELTA are held fixed by default when performing the fit). Constant parameters are specified by setting PARINFO[i].fixed to 1 within the FITMTF_KECK procedure (see documentation for MPFIT and MPFITFUN).
- PERROR: A structure of formal error in the best fit
parameters, as determined by MPFIT. Parameters that are not included in the fit or are held fixed during the fit return an error of 0.
- COVAR: The parameter covariance matrix, of size N x N, where
N is the number of fit parameters supplied to MPFIT, the values of which depend on the order of the vector of input parameters supplied to MPFIT. (See documentation for MPFIT and order of FCNARGS as defined within this procedure.)
- CHISQ: The quantity (RESIDS/ERROR)^2, where
RESIDS = POWER - BESTFIT, and POWER and ERROR are the vectors restored from FILENAME (see above). CHISQ is calculated ignoring data at NU < CLIP.
NITER: Number of iterations performed by the fitting routine.
- PROCEDURE CALLS:
MPFITFUN, MPFIT, T_PERFECT_KECK
- EXAMPLE:
read in a fully reduced H-band NIRC2 image im = READFITS(‘myimage.fits’)
calculate its power spectrum p = {lambda:1.65e-6, D:10.99, F:557.0, APIX:27e-6} GETMTF, im, p, nu, power, error, spdist SAVE, nu, power, error, spdist, filename=’mtfdata.sav’
fit an MTF to this data startp = {wave:1.65e-6, D:10.99, F:557.0, Apix:27e-6, $
pupil:’largehex’, L0:30.0, sigma:0.56, $ w:1.3, delta:0.0, cmult:1.0, N:1e-5, r0:0.5}
FITMTF_KECK, ‘mtfdata.sav’, bestfit_params, start=startp
zero in on the best fit parameters by editing FITMTF_KECK to perform the fit using a smaller step size to MPFIT. Change PARINFO[*].relstep from 0.20 to 0.02, recomplie FITMTF_KECK, and perform the fit again using the previous best fit parameters as the new starting parameters. FITMTF_KECK, ‘mtfdata.sav’, bestfit_params2, start=bestfit_params
calculate the encircled energy for the PSF in image ‘myimage.fits’ at a radius of 25 pixels (at the 0.01 arcsec/pix NIRC2 platescale). MTF2EE, bestfit_params2, 25.0, EE print, EE
compute the best fit power spectrum PSPEC = MTFFUNC_KECK(nu, bestfit_params2, spdist=spdist) plot, nu, power, /ylog, psym=4 oplot, nu, pspec
plot the best fit MTF T = sqrt(MTFFUNC_KECK(nu, bestfit_params2) plot, nu, T, /ylog
- MODIFICATION HISTORY:
Written by Christopher D. Sheehy, January 2006. Added “niter” keyword, Nate McCrady, May 17, 2007.
- kai.mtf.mtf.t_perfect_keck(x, p, pupil=None)[source]
- NAME:
T_PERFECT_KECK
- PURPOSE:
Numerically computes a 1-D approximation to the 2-D diffraction limited MTF of the segmented Keck pupil, appropriate for the NIRC2 camera.
- CATEGORY:
???
- CALLING SEQUENCE:
RESULT = T_PERFECT_KECK(NU, D, [PUPIL=PUPIL])
- INPUTS:
- NU: Normalized spatial frequency in the image plane, in
units of D/lambda.
- D: The diameter of the Keck pupil, in meters, to which the
spatial frequencies are normalized, i.e. not necessarily the oft-quoted effective diameter of 10 meters. If D is a scalar or a 1-element array, this value is used. Otherwise D must be a structure with the tag “D” defined, as per the definition of PARAMS in MTFFUNC_KECK.
- KEYWORD PARAMETERS:
- PUPIL: Set this keyword to a string to select the
- NIRC2 pupil-stop. Available choices are
‘OPEN’ ‘LARGEHEX’ ‘MEDIUMHEX’ ‘SMALLHEX’ ‘INCIRCLE’
If this keyword is not set, the default pupil is ‘LARGEHEX’. (See documentation for NIRC2PUPIL.)
- OUTPUTS:
RESULT: The diffraction limited MTF (N.B. not the square of the MTF).
- PROCEDURE:
Retrieves a pupil image from NIRC2PUPIL
Computes the 2-D autocorrelation function of the pupil
Radially bins and averages the 2-D autocorrelation function into a 1-D MTF.
Interpoates the 1-D MTF onto the grid of normalized spatial frequencies, NU, defined by the user.
- PROCEDURE CALLS:
NIRC2PUPIL(), CONVOLVE()
- MODIFICATION HISTORY:
Written by Christopher D. Sheehy, January 2006. Commented by Nate McCrady, January 2008.
- kai.mtf.mtf.nirc2pupil(npix=256, du=None, pmsname='largehex', pmrangl=0.0)[source]
- NAME:
NIRC2PUPIL
- PURPOSE:
Calculate NIRC2 pupil image
- EXPLANATION:
Calculate pupil image for any pupil stop, pupil angle, and image scale, for use by NIRC2PSF in determining theoretical PSF.
- CALLING SEQUENCE:
result = NIRC2PUPIL( [NPIX=, DU=, PMSNAME=, PMRANGL= ])
- INPUTS:
none.
- OUTPITS:
result = binary image of pupil
- OPTIONAL INPUT KEYWORDS:
NPIX = size of pupil image, in pixels
DU = platescale of pupil image, in m/pixel at the telescope primary
PMSNAME = pupil stop name, eg. ‘largehex’ (the default).
- PMRANGL = pupil drive’s angular position (for rotated pupil images).
NOT TESTED. There could be an offset and/or a sign flip needed!
- EXAMPLE:
pupil = NIRC2PUPIL(npix=512, du=0.05, PMSNAME=’open’)
- ERROR HANDLING:
none
- RESTRICTIONS:
none
- NOTES:
- The dimentions are based on Keck KAON 253 and the NIRC2 pupil
stop drawings.
- PROCEDURES USED:
none
- MODIFICATION HISTORY:
Original writen May 2004, A. Bouchez, W.M. Keck Observatory
- kai.mtf.mtf.dist_circle(size, center=None)[source]
” NAME:
DIST_CIRCLE
- PURPOSE:
Form a square array where each value is its distance to a given center.
- EXPLANATION:
Returns a square array in which the value of each element is its distance to a specified center. Useful for circular aperture photometry.
- CALLING SEQUENCE:
DIST_CIRCLE, IM, N, [ XCEN, YCEN, /DOUBLE ]
- INPUTS:
- N = either a scalar specifying the size of the N x N square output
array, or a 2 element vector specifying the size of the N x M rectangular output array.
- OPTIONAL INPUTS:
- XCEN,YCEN = Scalars designating the X,Y pixel center. These need
not be integers, and need not be located within the output image. If not supplied then the center of the output image is used (XCEN = YCEN = (N-1)/2.).
- OUTPUTS:
- IM - N by N (or M x N) floating array in which the value of each
pixel is equal to its distance to XCEN,YCEN
- OPTIONAL INPUT KEYWORD:
- /DOUBLE - If this keyword is set and nonzero, the output array will
be of type DOUBLE rather than floating point.
- EXAMPLE:
Total the flux in a circular aperture within 3’ of a specified RA and DEC on an 512 x 512 image IM, with a header H.
IDL> adxy, H, RA, DEC, x, y Convert RA and DEC to X,Y
IDL> getrot, H, rot, cdelt CDELT gives plate scale deg/pixel IDL> cdelt = cdelt*3600. Convert to arc sec/pixel IDL> dist_circle, circle, 512, x, y ;Create a distance circle image IDL> circle = circle*abs(cdelt[0]) ;Distances now given in arcseconds IDL> good = where(circle LT 180) ;Within 3 arc minutes IDL> print,total( IM[good] ) Total pixel values within 3’
- RESTRICTIONS:
The speed of DIST_CIRCLE decreases and the the demands on virtual increase as the square of the output dimensions. Users should dimension the output array as small as possible, and re-use the array rather than re-calling DIST_CIRCLE
- MODIFICATION HISTORY:
Adapted from DIST W. Landsman March 1991 Allow a rectangular output array W. Landsman June 1994 Converted to IDL V5.0 W. Landsman September 1997 Add /DOUBLE keyword, make XCEN,YCEN optional W. Landsman Jun 1998
- kai.mtf.mtf.t_perfect(x, ee)[source]
- NAME:
T_PERFECT
- PURPOSE:
Computes the analytic diffraction limited MTF of a circular pupil with a circular central obscuration.
- CATEGORY:
What goes here?
- CALLING SEQUENCE:
RESULT = T_PERFECT(NU, PUPIL)
- INPUTS:
- NU: Normalized spatial frequency in the image plane, in
units of D/lambda where D is the pupil diameter and lambda is the observing wavelength need not be regularly gridded
- PUPIL: The pupil’s central obscuration, defined as the
ratio of the obscuration’s diameter to the pupil’s diameter. If PUPIL is a scalar or a 1-element array, this value is used. Otherwise PUPIL must be a structure with the tag “PUPIL” defined, as per the definition of PARAMS in MTFFUNC_KECK.
- OPTIONAL INPUTS:
NONE
- KEYWORD PARAMETERS:
NONE
- OUTPUTS:
RESULT: The diffraction limited pupil MTF (N.B. not the square of the MTF)
- OPTIONAL OUTPUTS:
NONE
- MODIFICATION HISTORY:
Written by Christopher D. Sheehy, January 2006.
- kai.mtf.mtf.t_pix(x, p)[source]
- NAME:
T_PIX
- PURPOSE:
Analytically computes the MTF of an ideal square pixel, i.e. the detector MTF.
- CATEGORY:
???
- CALLING SEQUENCE:
RESULT = T_PIX(NU, PARAMS)
- INPUTS:
- NU: Normalized spatial frequency in the image plane, in
units of D/lambda.
- PARAMS: Must be a structure containing the tags “lambda”,
“D”, “F”, and “A” as defined in the documentation for MTFFUNC_KECK.
- OPTIONAL INPUTS:
NONE
- KEYWORD PARAMETERS:
NONE
- OUTPUTS:
The detector MTF (N.B. not the square of the MTF)
- PROCEDURE CALLS:
SINC()
- MODIFICATION HISTORY:
Written by Christopher Sheehy, January 2006.
- kai.mtf.mtf.t_atmos_ao(x, p)[source]
- NAME:
T_ATMOS_AO
- PURPOSE:
Computes the AO filtered atmospheric MTF assuming a modified Kolmogorov atmospheric phase error power spectrum with a finite outer scale of turbulence.
- CATEGORY:
- CALLING SEQUENCE:
RESULT = T_ATMOS_AO(NU, PARAMS)
- INPUTS:
- NU: Normalized spatial frequency in the image plane, in
units of D/lambda.
- PARAMS: A structure of parameters, defined in the
documentation for MTFFUNC_KECK
- OPTIONAL INPUTS:
NONE
- KEYWORD PARAMETERS:
NONE
- OUTPUTS:
RESULT: The AO+atmosphere MTF the same size as NU.
- RESTRICTIONS:
NU must be greater than zero.
- PROCEDURE CALLS:
STRUC_FUNC()
- PROCEDURE:
Computes the structure function for the AO filtered Kolmogorov power spectrum using STRUC_FUNC and exponentiates to yield the atmosphere + AO MTF.
- MODIFICATION HISTORY:
Written by Christopher D. Sheehy, January 2006.
- kai.mtf.mtf.phi_atmos_ao(x, p, unmod=False, tat=False)[source]
- NAME:
PHI_ATMOS_AO
- PURPOSE:
Calculates the AO filtered atmospheric power spectrum for spatial frequencies in the pupil plane, Phi_AO = Phi*(1-H)^2 where Phi is the unfiltered atmospheric power spectrum and H is the Fourier transform of the deformable mirror’s (DM’s) influence function. The default behavior is to use modified Kolmogorov power spectrum with finite outer scale and the influence function for the Keck AO system’s DM.
- CATEGORY:
???
- CALLING SEQUENCE:
Result = PHI_ATMOS_AO(KAPPA, PARAMS, [unmod=unmod, tat=tat])
- INPUTS:
- KAPPA: A vector of spatial frequencies in the pupil plane,
in m^-1
- PARAMS: A structure of parameters as defined in the
documentation for MTFFUNC_KECK
- KEYWORD PARAMETERS:
- /UNMOD: Set this keyword to use an unmodified Kolmogorov
atmospheric power spectrum, i.e. with an infinite outer scale.
- /TAT: Set this keyword to use a modified Tatarski power
spectrum, i.e. one with both a finite outer scale and finite inner scale (WARNING: UNTESTED). If this keyword is invoked, the PARAMS structure must contain an extra tag, “Inner:”, that is the inner scale of turbulence in meters.
- OUTPUTS:
- Result: The AO filtered atmospheric power spectrum, of
evaluated at and the same size as KAPPA.
- RESTRICTIONS:
If the /UNMOD keyword is set, an input KAPPA of zero will cause a divide by 0 error, and RESULT will be Infinity, because the power at zero spatial frequency for an infinite outer scale is infinity.
Works for the Keck DM’s influence function. If the user wishes to use a different influence function, replace the call to FT_INFL_FUNC within the routine with another function that returns the Fourier transform of the appropriate influence function. This function should take as inputs KAPPA and PARAMS (the user may add other tags to the PARAMS structure as necessary) and return the FT of the influence function as projected onto the pupil plane, evaluated at the inpute KAPPA.
- PROCEDURE CALLS:
PHI__ATMOS(), FT_INFL_FUNC()
- MODIFICATION HISTORY:
Written by Christopher Sheehy, January 2006.
- kai.mtf.mtf.phi_atmos(x, p, tat=False, unmod=False)[source]
- NAME:
PHI_ATMOS
- PURPOSE:
Calculates a modified Kolmogorov atmospheric phase error power spectrum with finite outer scale of turbulence.
- CATEGORY:
???
- CALLING SEQUENCE:
RESULT = PHI_ATMOS(KAPPA, PARAMS, [unmod=unmod, tat=tat])
- INPUTS:
- KAPPA: A vector of spatial frequencies in the pupil plane,
in m^-1, at which the power spectrum is evaluated (need not be regularly gridded).
- PARAMS: A structure of parameters as definted in the
documentation for MTFFUNC_KECK
- KEYWORD PARAMETERS:
- /UNMOD: Set this keyword to return an unmodified Kolmogorov
power spectrum, i.e. one with an infinite outer scale.
- /TAT: Set this keyword to return a modified Tatarski power
spectrum, i.e. one with both a finite outer scale and finite inner scale (WARNING: UNTESTED). If this keyword is invoked, the PARAMS structure must contain an extra tag, “Inner:”, that is the inner scale of turbulence in meters.
- OUTPUTS:
- RESULT: The Kolmogorov atmospheric power spectrum, of same
size as input KAPPA.
- RESTRICTIONS:
If the /UNMOD keyword is set, an input KAPPA of zero will cause a divide by 0 error, and RESULT will be Infinity, because the power at zero spatial frequency for an infinite outer scale is infinity.
- PROCEDURE:
The Kolmogorov spectrum with inifinte outer scale is calculated. If the /UNMOD keyword is set, this is immediately returned.
The Kolmogorov spectrum with finite outer scale is calculated. Since the power at spatial scales much less than the outer scale should be left unaffected, the spectrum is normalized to have the same power at a very high spatial frequency, 100 m^-1.
- MODIFICATION HISTORY:
Written by Christopher Sheehy, January 2006
- kai.mtf.mtf.ft_infl_func(x, p)[source]
- NAME:
FT_INFL_FUNC
- PURPOSE:
Evaltuates the Fourier transform of the Keck AO system’s deformable mirror at given input spatial frequency in the pupil plane. Uses the functional form for the influence function given by van Dam, et al., 2004, Applied Optics, 43, 5452.
- CATEGORY:
???
- CALLING SEQUENCE:
Result = FT_INFL_FUNC(KAPPA, PARAMS)
- INPUTS:
- KAPPA: Spatial frequency in the pupil plane of the telescope
in m^-1.
- PARAMS: A structure of parameters as defined in the
documentation for MTFFUNC_KECK. Only SIGMA and W need be defined.
- OUTPUTS:
- Result: The FT of the influence function, evaluated at and
of the same size as KAPPA. The output is multiplied by W before output. W=2 gives perfect AO correction at zero spatial frequency.
- PROCEDURE:
The FT of the influence function has a set functional form, the difference of two Gaussians, and depends only on the parameter SIGMA (as defined in PARAMS) that is on the order of the separation between DM actuators.
The result is multiplied by a constant scaling factor w, defined in PARAMS, before being output.
- MODIFICATION HISTORY:
Written by Christopher Sheehy
- kai.mtf.mtf.structure_function(rr, pp, phi_call=phi_atmos_ao)[source]
- “
- NAME:
STRUC_FUNC
- PURPOSE:
Calculates the structure function, D(r), where r is the distance between two points in the pupil plane of the telescope in meter. Default behavior is to calculate D(r) for an AO corrected Kolmogorov atmospheric power spectrum with finite outer scale. However, the user can define any arbitrary atmospheric power spectra for which to calculate D(r).
- CATEGORY:
???
- CALLING SEQUENCE:
RESULT = STRUC_FUNC(R, PARAMS, [phi_call=phi_call])
- INPUTS:
R: A vector of radii in the pupil plane, in meters
PARAMS: A structure of parameters as defined in the documentation for MTFFUNC_KECK
- OPTIONAL INPUTS:
NONE
- KEYWORD PARAMETERS:
- PHI_CALL: The default behavior of STRUC_FUNC, i.e. not
defning PHI_CALL, is to calculate the structure function assuming a modified Kolmogorov power spectrum with a finite outer scale and corrected by adaptive optics. If the user wishes to find D(r) for a different power spectrum, PHI_CALL should be a string that, as executed, calls an IDL function that returns the power spectrum for input spatial frequencies KAPPA (as defined in the documentation for PHI_ATMOS/PHI_ATMOS_AO). This function must be structured as follows:
- FUNCTION MYFUNCT, KAPPA, PARAMS, KEYWORDS=…
- (compute the atmospheric power spectrum PHI
at given X for input parameters PARAMS) RETURN, PHI
END
The PARAMS input to the function is the same structure as the PARAMS input into STRUC_FUNC.
PHI_CALL MUST HAVE ‘k’ AS THE SPATIAL FREQUENCY VARIABLE NAME ‘k’ AND ‘p’ AS THE PARAMETER STRUCTURE VARAIBLE NAME!
Example: The function PHI_ATMOS returns the uncorrected atmospheric power spectrum, and would be called as such:
IDL> x=findgen(10) IDL> phi=PHI_ATMOS(x,params)
where params has already been defined and is a structure containing information for PHI_ATMOS to be able to calculate the power spectrum. In the call to STRUC_FUNC, setting the keyword
PHI_CALL = ‘PHI_ATMOS(k,p)’
forces STRUC_FUNC to use this power spectrum in calculating D(r).
PHI_ATMOS also accepts keywords for instance
IDL> phi=PHI_ATMOS(x,params,/unmod)
returns an uncorrected power spectrum with an infinite outer scale. In this case, one would set the keyword
PHI_CALL = ‘PHI_ATMOS(k,p,/unmod)’
Leaving the keyword PHI_CALL undefined is equivalent to setting
PHI_CALL = ‘PHI_ATMOS_AO(k,p)
- OUTPUTS:
RESULT: A vector of same size as R, the structure function evaluated at R
- PROCEDURE CALLS:
PHI_ATMOS_AO(), D_R(), QPINT1D()
- PROCEDURE:
Utilizes the adaptive 1-d integration routine QPINT1D, written by Craig Markwardt and available from http://cow.physics.wisc.edu/~craigm/idl/idl.html
- MODIFICATION HISTORY:
Written by Christopher Sheehy, January 2006.
- kai.mtf.mtf.mtf2psf(par, sz, perfect=False)[source]
” NAME:
MTF2PSF
- PURPOSE:
Computes the adaptive optics PSF for the modulation transfer function (MTF) defined by a set of user supplied input parameters. The PSF is circularly symmetric, i.e. azimuthally averaged.
- CATEGORY:
???
- CALLING SEQUENCE:
MTF2PSF, Params, Size, Psf2D, PSF1D
- INPUTS:
- Params: A structure of parameters defined as follows, and
which may contain more tags than listed here:
params.lambda - observing wavelength in meters params.f - effective focal length at detector
in meters
- params.D - telsscope pupil diameter in meters,
i.e. the D/lambda at which normalized spatial frequency nu=1
params.Apix - width of detector pixel in meters params.pupil - a string equal to the name of
the pupil-stop of the NIRC2 camera (see documentation for T_PERFECT_KECK for a list of available pupil-stop names) or for a circular pupil, the scalar floating point value of the pupil’s central obscuration.
- params.L0 - the outer scale of turbluence, in
meters, for a modified Kolmogorov spectrum
- params.sigma - the width of the AO system
deformable mirror’s (DM’s) influence function as projected onto the pupil plane, in meters.
- params.w - scaling factor for the influence
function’s Fourier transform mimics variable AO correction
params.delta - wavefront measurement error params.cmult - constant scaling factor of the output
MTF
- params.N - additive constant to output MTF
representing a noise floor
- params.r0 - wavelength specific Fried
parameter in meters
- Size: A scalar, the radius of the output PSF in
arcseconds. For instance, is Size = 1.0 and the platescale at the detector is .01 arcsec/pixel, the output PSF is a 200 x 200 element array.
- OPTIONAL INPUTS:
NONE
- KEYWORD PARAMETERS:
- /PERF: If this keyword is set, the PSF is calculated from
the diffraction limited pupil MTF.
- OUTPUTS:
- Psf2D: A 2-dimensional array, the azimuthally averaged AO
PSF.
- OPTIONAL OUTPUTS:
- Psf1D: A 1-dimensional array, the 1-D PSF whose value at
each element corresponds to the value of the PSF at the corresponding pixel.
- PROCEDURE CALLS:
MTFFUNC_KECK(), INT_TABULATED()
- PROCEDURE:
For the given input parameters Params, the 1-D MTF is computed via the procedure MTFFUNC_KECK. The 1-D PSF is then given by the integral
1/
- PSF(w) = | MTF(nu) * nu * BesselJ_0(2*PI*w*nu)* d nu,
0/
where w is dimensionless angular distance from the PSF center in units of (lambda/D), and nu is normalized spatial frequency in the image plane. The 1-D PSF is computed, 5x oversampled w.r.t. the detector platescale. (The platescale is determined from the input parameters, Apix / f.) From this oversampled 1-D PSF, the circularly symmetric 2-D PSF is constructed.
- EXAMPLE:
Compute H-band NIRC2 PSF for r0 = 15 cm:
r0 goes as (lambda)^(6/5), so the K-band r0 in meters is 0.15 * (2.2 / 0.5)^(6./5.), since r0 = 15 cm is defined for a wavelength of 500 nm.
Set up the input parameters:
- p = {wave:2.2e-6, F:557.0, D:10.99, $
Apix:27e-6, pupil:’largehex’, L0:30.0, $ sigma:0.56, w:1.5, delta:0.0, cmult:1.0, N:1e-5, $ r0:0.888}
sz = 1.0 return a PSF with a radius of 1 arcsecond MTF2PSF, p, sz, psf2, psf1 tvscl, psf2 plot, psf1
nu = findgen(100)/99. T = sqrt(MTFFUNC_KECK(nu, p)) compute the PSF’s corresponding MTF plot, nu, T
compute the PSF for identical seeing conditions but with no AO correction
p.w = 0 no AO correction MTF2PSF, p, sz, psf2_noAO, psf1_noAO
compute the diffraction limited PSF
MTF2PSF, p, sz, psf2_perf, psf1_perf, /perf
There is a subtle difference between setting the /perf keyword to MTF2PSF and setting r0 to some extremely large and unphysical value to mimic diffraction limited seeing. The former computes the PSF from the pupil MTF, while the latter uses the product of the puipl MTF, the atmospheric/AO MTF (which is essentially unity) and the detector MTF. The detector MTF is a broad sinc function, and its resulting effect on the PSF is small. In other words, setting the /perf keyword fails to take into account the effect of the detector on the PSF.
- MODIFICATION HISTORY:
Written by Christopher Sheehy, January 2006.
- kai.mtf.mtf.mtf2ee(par, pixx, perfect=False)[source]
” NAME:
MTF2EE
- PURPOSE:
Calculates the AO PSF’s encircled energy curve from the AO corrected modulation transfer function.
- CATEGORY:
???
- CALLING SEQUENCE:
MTF2EE, Params, Pix, EE
- INPUTS:
- Params: A structure of parameters, defined as in the
documentation for MTFFUNC_KECK.
- Pix: A vector of radii, in pixels, at which the encircled
energy curve of growth is calculated. The pixel scale in pixels/arcsecond is calculated as (Params.APIX / Params.F)*206265.
- OPTIONAL INPUTS:
NONE
- KEYWORD PARAMETERS:
- /Perf: If this keyword is set, the returned curve of growth
is for the diffraction limited PSF as calculated from the pupil MTF.
- OUTPUTS:
- EE: A vector of size equal to Pix the curve of growth
evaluated at input Pix
- OPTIONAL OUTPUTS:
NONE
- PROCEDURE CALLS:
MTFFUNC_KECK(), INT_TABULATED()
- PROCEDURE:
For the given input parameters Params, the 1-D MTF is computed via the procedure MTFFUNC_KECK. The encirled energy curve of growth is then given by the integral
1/
- EE(w) = (2*Pi*w) | MTF(nu) * BesselJ_1(2*PI*w*nu)* d nu,
0/
where w is dimensionless angular distance from the PSF center in units of (lambda/D), and nu is normalized spatial frequency in the image plane.
- MODIFICATION HISTORY:
Written by Christopher D. Sheehy, January 2006.
- kai.mtf.mtf.strehl(par)[source]
- NAME:
STREHL
- PURPOSE:
Computes the Strehl ratio of an AO PSF from its corresponding modulation transfer function (MTF).
- CATEGORY:
???
- CALLING SEQUENCE:
sr = STREHL(params)
- INPUTS:
- Params: A structure of parameters used to compute the AO
MTF, as defined in the documentation for MTFFUNC_KECK.
- KEYWORD PARAMETERS:
NONE
- OUTPUTS:
The scalar strehl ratio for the given input parameters
- PROCEDURE CALLS:
MTFFUNC_KECK(), INT_TABULATED()
- PROCEDURE:
For the given input parameters, the MTF, T, is calculated via MTFFUNC_KECK() along with the diffraction limited MTF, Tperf. The strehl ratio, defined as the ratio of the height of the observed PSF to the diffraction limited PSF is calculated as (see documentation for MTF2PSF)
- 1/
- T(nu)*nu d nu
0/
- Sr = ——————– .
- 1/
- Tperf(nu)*nu d nu
0/
- MODIFICATION HISTORY:
Written by Christopher D. Sheehy, January 2006.