updates: igor 7, map projections, hemi cuts, longitudinal section
- pearl procedures compile under igor 7. some features may not work, e.g. 3D graphics with gizmo. - add orthographic map projection to angle scans. - add functions for azimuthal and polar cuts through hemispherical scan. - add function to load longitudinal section from pshell data file.
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@ -808,9 +808,9 @@ function convert_angles_ttpa2polar(theta, tilt, phi, analyser, polar, azi)
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// this is simply a polar-cartesian mapping, independent of the manipulator
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// phi=0 is in the polar rotation plane
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make /n=(3,na) /d /free w_orig_polar, w_orig_cart, w_rot_cart, w_rot_polar
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w_orig_polar[0] = radius
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w_orig_polar[1] = analyser[q]
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w_orig_polar[2] = 0
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w_orig_polar[0][] = radius
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w_orig_polar[1][] = analyser[q]
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w_orig_polar[2][] = 0
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polar2cart_wave(w_orig_polar, w_orig_cart)
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// if the angle-dispersive axis was horizontal, we'd need to rotate the detector
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//rotate_z_wave(w_orig_cart, 90)
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@ -1905,21 +1905,46 @@ function /s display_scanlines(nickname, alpha_lo, alpha_hi, m_theta, m_tilt, m_p
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return graphname
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end
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static constant kProjScaleLinear = 2
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/// @page PageProjections Projections
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///
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/// the functions of the anglescan package support the following map projections.
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/// for a description of the different projections, see, for example,
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/// https://en.wikipedia.org/wiki/Map_projection
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///
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/// | Selector | Projection | Function | Properties |
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/// | :----: | :----: | :----: | :---- |
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/// | kProjDist = 0 | azimuthal equidistant | r = c * theta | radius is proportional to polar angle. |
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/// | kProjStereo = 1 | stereographic | r = c * tan theta/2 | circles on sphere map to circles. |
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/// | kProjArea = 2 | azimuthal equal-area | r = c * sin theta/2 | preserves area measure. |
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/// | kProjGnom = 3 | gnomonic | r = c * tan theta | great circles map to straight lines. |
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/// | kProjOrtho = 4 | orthographic | r = c * sin theta | k-space mapping in ARPES and LEED. |
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///
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/// the projections in this package are defined for 0 <= theta < 90.
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///
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constant kProjDist = 0
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constant kProjStereo = 1
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constant kProjArea = 2
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constant kProjGnom = 3
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constant kProjOrtho = 4
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static constant kProjScaleDist = 2
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static constant kProjScaleStereo = 2
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static constant kProjScaleAzim = 2
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static constant kProjScaleArea = 2
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// scaled so that radius(gnom) = radius(stereo) for polar = 88
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static constant kProjScaleGnomonic = 0.06744519021
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static constant kProjScaleGnom = 0.06744519021
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static constant kProjScaleOrtho = 2
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/// calculate the projected polar angle
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///
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/// @param polar polar angle in degrees
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///
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/// @param projection mapping function from polar to cartesian coordinates
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/// @arg 0 linear
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/// @arg 1 stereographic (default)
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/// @arg 2 azimuthal
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/// @arg 3 gnomonic (0 <= polar < 90)
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/// @param projection mapping function from polar to cartesian coordinates.
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/// see @ref PageProjections for details.
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/// @arg kProjDist = 0 azimuthal equidistant
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/// @arg kProjStereo = 1 stereographic (default)
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/// @arg kProjArea = 2 azimuthal equal-area
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/// @arg kProjGnom = 3 gnomonic (0 <= polar < 90)
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/// @arg kProjOrtho = 4 orthographic
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///
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/// @return projected radius.
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/// the radius is scaled such that grazing emission maps to 2.
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@ -1933,17 +1958,20 @@ threadsafe function calc_graph_radius(polar, [projection])
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variable radius
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switch(projection)
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case 1: // stereographic
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case kProjStereo: // stereographic
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radius = kProjScaleStereo * tan(polar / 2 * pi / 180)
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break
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case 2: // azimuthal
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radius = kProjScaleAzim * cos((180 - polar) / 2 * pi / 180)
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case kProjArea: // equal area
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radius = kProjScaleArea * sin(polar / 2 * pi / 180)
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break
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case 3: // gnomonic
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radius = polar < 90 ? kProjScaleGnomonic * tan(polar * pi / 180) : inf
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case kProjGnom: // gnomonic
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radius = polar < 90 ? kProjScaleGnom * tan(polar * pi / 180) : inf
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break
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default: // linear
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radius = kProjScaleLinear * polar / 90
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case kProjOrtho: // orthographic
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radius = kProjScaleOrtho * sin(polar * pi / 180)
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break
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default: // equidistant
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radius = kProjScaleDist * polar / 90
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endswitch
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return radius
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@ -1955,10 +1983,13 @@ end
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///
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/// @param x, y projected Cartesian coordinate
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///
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/// @param projection mapping function from polar to cartesian coordinates
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/// @arg 0 linear
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/// @arg 1 stereographic (default)
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/// @arg 2 azimuthal
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/// @param projection mapping function from polar to cartesian coordinates.
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/// see @ref PageProjections for details.
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/// @arg kProjDist = 0 azimuthal equidistant
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/// @arg kProjStereo = 1 stereographic (default)
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/// @arg kProjArea = 2 azimuthal equal-area
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/// @arg kProjGnom = 3 gnomonic (0 <= polar < 90)
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/// @arg kProjOrtho = 4 orthographic
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///
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/// @returns polar angle in degrees
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///
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@ -1976,17 +2007,20 @@ threadsafe function calc_graph_polar(x, y, [projection])
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radius = sqrt(x^2 + y^2)
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switch(projection)
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case 1: // stereographic
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case kProjStereo: // stereographic
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polar = 2 * atan(radius / kProjScaleStereo) * 180 / pi
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break
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case 2: // azimuthal
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polar = 180 - 2 * acos(radius / kProjScaleAzim) * 180 / pi
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case kProjArea: // equal area
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polar = 2 * asin(radius / kProjScaleArea) * 180 / pi
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break
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case 3: // gnomonic
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polar = atan(radius / kProjScaleGnomonic) * 180 / pi
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case kProjGnom: // gnomonic
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polar = atan(radius / kProjScaleGnom) * 180 / pi
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break
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default: // linear
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polar = 90 * radius / kProjScaleLinear
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case kProjOrtho: // orthographic
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polar = asin(radius / kProjScaleOrtho) * 180 / pi
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break
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default: // equidistant
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polar = 90 * radius / kProjScaleDist
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endswitch
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return polar
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@ -1997,10 +2031,13 @@ end
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/// @param x, y projected Cartesian coordinate
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///
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/// @param projection mapping function from polar to cartesian coordinates.
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/// projections 0-2 have no effect on the azimuthal coordinate.
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/// @arg 0 linear
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/// @arg 1 stereographic (default)
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/// @arg 2 azimuthal
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/// all supported projections are azimuthal, they have no effect on the azimuthal coordinate.
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/// see @ref PageProjections for details.
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/// @arg kProjDist = 0 azimuthal equidistant
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/// @arg kProjStereo = 1 stereographic (default)
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/// @arg kProjArea = 2 azimuthal equal-area
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/// @arg kProjGnom = 3 gnomonic (0 <= polar < 90)
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/// @arg kProjOrtho = 4 orthographic
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///
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/// @param zeroAngle zeroAngleWhere parameter of polar graphs
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/// @arg 0 (default) zero is at the 3 o'clock position
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@ -2586,4 +2623,158 @@ function import_tpi_scan(nickname, theta, phi, intensity, [folding, npolar, nogr
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endfor
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display_hemi_scan(nickname)
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end
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end
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/// extract a polar cut from a hemispherical scan.
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///
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/// for each polar angle, the function first extracts all azimuthal angles.
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/// the intensity is then interpolated between the nearest neighbours of the given azimuth.
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///
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/// the hemi grid must have been created in the current data folder by the make_hemi_grid function.
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/// correct ordering is required.
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///
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/// @param nickname name of the scan dataset.
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/// can be empty if no prefix is used.
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/// the dataset must be in the current datafolder.
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///
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/// @param azim azimuthal angle in degrees
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///
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/// @return reference of the created wave.
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/// the wave has the same name as the intensity wave of the dataset
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/// with the suffix "_azi" and the azimuthal angle rounded to integer.
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/// it is created in the same datafolder as the original data.
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///
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function /wave hemi_polar_cut(nickname, azim)
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string nickname
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variable azim
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if (strlen(nickname))
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string s_prefix = nickname + "_"
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string s_int = s_prefix + "i"
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else
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s_prefix = ""
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s_int = "values"
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endif
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string s_totals = s_prefix + "tot"
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string s_weights = s_prefix + "wt"
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string s_polar = s_prefix + "pol"
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string s_azim = s_prefix + "az"
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string s_index = s_prefix + "index"
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string s_theta = s_prefix + "th"
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string s_dphi = s_prefix + "dphi"
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string s_nphis = s_prefix + "nphis"
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string s_cut
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sprintf s_cut, "%s_azi%03u", s_int, round(azim)
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wave w_polar = $s_polar
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wave w_azim = $s_azim
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wave w_values = $s_int
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wave w_totals = $s_totals
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wave w_weights = $s_weights
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wave w_index = $s_index
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wave w_theta = $s_theta
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wave w_dphi = $s_dphi
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wave w_nphis = $s_nphis
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variable npol = numpnts(w_theta)
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variable ipol
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variable pol_st = abs(w_theta[1] - w_theta[0])
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variable pol
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variable pol1, pol2
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variable nsel
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make /n=(npol) /o $s_cut
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wave w_cut = $s_cut
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setscale /i x w_theta[0], w_theta[numpnts(w_theta)-1], "deg", w_cut
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make /n=1 /free azi_slice
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make /n=1 /free values_slice
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for (ipol = 0; ipol < npol; ipol += 1)
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pol = w_theta[ipol]
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pol1 = pol - pol_st / 2
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pol2 = pol + pol_st / 2
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extract /free /indx w_polar, sel, (pol1 < w_polar) && (w_polar <= pol2)
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nsel = numpnts(sel)
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if (nsel > 0)
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redimension /n=(nsel+2) azi_slice, values_slice
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azi_slice[1, nsel] = w_azim[sel[p-1]]
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azi_slice[0] = azi_slice[nsel] - 360
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azi_slice[nsel+1] = azi_slice[1] + 360
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values_slice[1, nsel] = w_values[sel[p-1]]
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values_slice[0] = values_slice[nsel]
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values_slice[nsel+1] = values_slice[1]
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w_cut[ipol] = interp(azim, azi_slice, values_slice)
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else
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w_cut[ipol] = nan
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endif
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endfor
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return w_cut
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end
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/// extract an azimuthal cut from a hemispherical scan
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///
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/// the function extracts all azimuthal angles that are present for the given polar angle.
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///
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/// the hemi grid must have been created in the current data folder by the make_hemi_grid function.
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/// correct ordering is required.
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///
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/// @param nickname name of the scan dataset.
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/// can be empty if no prefix is used.
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/// the dataset must be in the current datafolder.
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///
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/// @param pol polar angle in degrees
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///
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/// @return reference of the created wave.
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/// the wave has the same name as the intensity wave of the dataset
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/// with the suffix "_azi" and the azimuthal angle rounded to integer.
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/// it is created in the same datafolder as the original data.
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///
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function /wave hemi_azi_cut(nickname, pol)
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string nickname
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variable pol
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if (strlen(nickname))
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string s_prefix = nickname + "_"
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string s_int = s_prefix + "i"
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else
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s_prefix = ""
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s_int = "values"
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endif
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string s_totals = s_prefix + "tot"
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string s_weights = s_prefix + "wt"
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string s_polar = s_prefix + "pol"
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string s_azim = s_prefix + "az"
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string s_index = s_prefix + "index"
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string s_theta = s_prefix + "th"
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string s_dphi = s_prefix + "dphi"
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string s_nphis = s_prefix + "nphis"
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string s_cut
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sprintf s_cut, "%s_pol%03u", s_int, round(pol)
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wave w_polar = $s_polar
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wave w_azim = $s_azim
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wave w_values = $s_int
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wave w_totals = $s_totals
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wave w_weights = $s_weights
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wave w_index = $s_index
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wave w_theta = $s_theta
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wave w_dphi = $s_dphi
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wave w_nphis = $s_nphis
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variable pol_st = abs(w_theta[1] - w_theta[0])
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variable pol1, pol2
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variable nsel
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pol1 = pol - pol_st / 2
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pol2 = pol + pol_st / 2
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extract /free /indx w_polar, sel, (pol1 < w_polar) && (w_polar <= pol2)
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nsel = numpnts(sel)
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if (nsel > 0)
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make /n=(nsel) /o $s_cut
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wave w_cut = $s_cut
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w_cut = w_values[sel]
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setscale /i x w_azim[sel[0]], w_azim[sel[nsel-1]], "deg", w_cut
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return w_cut
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else
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return $""
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endif
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end
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