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update multifield doc to stpsf
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BradleySappington committed Dec 11, 2024
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"$$\\phi(x,y;u,v) = \\sum\\limits _j \\alpha_j\\left({u,v}\\right)Z_j\\left({x,y}\\right)$$\n",
"The field varying characteristic of the polynomial coefficents is captured by performing a second polynomial expansion on each of the coefficients,\n",
"$$\\alpha_j\\left(u,v\\right) = \\sum\\limits_k\\beta_{j,k}L_k\\left(u,v\\right),$$\n",
"where $\\beta_{j,k}$ is the coffiencient of this second expansion corresponding to the $j^{th}$ Zernike term and $L_k \\left(u,v\\right)$ is a set of polynomials that vary across field. The $L_k \\left(u,v\\right)$ polynomials are typically straightforward to compute at an arbitrary field point. While Zernike polynomials or other similar sets can be used here, we have elected to use a set of two-dimensional Legendre polynomials for this in WebbPSF since the instrument fields of interest are typically rectangular and the Legendres are orthonormal over a rectangular region."
"where $\\beta_{j,k}$ is the coffiencient of this second expansion corresponding to the $j^{th}$ Zernike term and $L_k \\left(u,v\\right)$ is a set of polynomials that vary across field. The $L_k \\left(u,v\\right)$ polynomials are typically straightforward to compute at an arbitrary field point. While Zernike polynomials or other similar sets can be used here, we have elected to use a set of two-dimensional Legendre polynomials for this in STPSF since the instrument fields of interest are typically rectangular and the Legendres are orthonormal over a rectangular region."
]
},
{
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"metadata": {},
"source": [
"Thus field dependence of the optical system of interest can be entirely characterized by a relatively small, two-dimensional matrix of $\\beta_{j,k}$ coefficients.\n",
"These coefficients have been precomputed for use in WebbPSF by using the most up-to-date CodeV models of the JWST optical telescope assembly (OTE). For the highest fidelity, a set of these coefficients is computed separately for each of the instrument fields."
"These coefficients have been precomputed for use in STPSF by using the most up-to-date CodeV models of the JWST optical telescope assembly (OTE). For the highest fidelity, a set of these coefficients is computed separately for each of the instrument fields."
]
},
{
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"metadata": {},
"source": [
"## Field Dependence in JWST\n",
"To build our field dependence model in WebbPSF, we have employed the as-built CodeV model of JWST derived from the nominal optical design for JWST, measurements of the figure of individual components, and end-to-end measurements of the OTE wavefront error conducted in the course of the JWST test campaign. In the figure below we show the wavefront at a selection of field points, generally in the corners of the instrument fields. The variation of wavefront with field angle is quite evident.\n"
"To build our field dependence model in STPSF, we have employed the as-built CodeV model of JWST derived from the nominal optical design for JWST, measurements of the figure of individual components, and end-to-end measurements of the OTE wavefront error conducted in the course of the JWST test campaign. In the figure below we show the wavefront at a selection of field points, generally in the corners of the instrument fields. The variation of wavefront with field angle is quite evident.\n"
]
},
{
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"cell_type": "markdown",
"metadata": {},
"source": [
"For practical use with WebbPSF, we are interested in the variation of the wavefront with field from the nominal wavefront defined in WebbPSF. To facilitate these, we subtract the wavefront modeled by CodeV at its (0,0) field point. In JWST $\\left(v_2,v_3\\right)$ field coordinates, this is at the location (0, -468 arcsec). The following figure shows the field-dependent wavefronts at the same points as above but with the nominal wavefront subtracted and plotted in the $\\left(v_2,v_3\\right)$ coordinate system. Residual piston, tip and tilt terms are also removed from the wavefront and are not modeled."
"For practical use with STPSF, we are interested in the variation of the wavefront with field from the nominal wavefront defined in STPSF. To facilitate these, we subtract the wavefront modeled by CodeV at its (0,0) field point. In JWST $\\left(v_2,v_3\\right)$ field coordinates, this is at the location (0, -468 arcsec). The following figure shows the field-dependent wavefronts at the same points as above but with the nominal wavefront subtracted and plotted in the $\\left(v_2,v_3\\right)$ coordinate system. Residual piston, tip and tilt terms are also removed from the wavefront and are not modeled."
]
},
{
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"cell_type": "markdown",
"metadata": {},
"source": [
"If we then use our polynomial-based WebbPSF model to calculate the wavefront variation at the same field points we have the following result.\n"
"If we then use our polynomial-based STPSF model to calculate the wavefront variation at the same field points we have the following result.\n"
]
},
{
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"source": [
"<img src=\"stpsf_field_dep.png\" width=\"1200\">\n",
"\n",
"<center>Figure 5: WebbPSF modeled wavefronts with nominal wavefront and piston, tip and tilt removed. JWST $\\left(v_2,v_3\\right)$ is the lateral coordinate system used here.\n",
"<center>Figure 5: STPSF modeled wavefronts with nominal wavefront and piston, tip and tilt removed. JWST $\\left(v_2,v_3\\right)$ is the lateral coordinate system used here.\n",
"</center>"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"## Model usage in WebbPSF"
"## Model usage in STPSF"
]
},
{
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"The model is implemented in the `_get_field_dependence_nominal_ote()` method of the `OTE_Linear_Model_WSS` class in the opds.py file of WebbPSF. WebbPSF will apply the field-dependence model automatically when used in the ordinary way. The following illustrates the calculation of a PSF that uses the field-dependent model"
"The model is implemented in the `_get_field_dependence_nominal_ote()` method of the `OTE_Linear_Model_WSS` class in the opds.py file of STPSF. STPSF will apply the field-dependence model automatically when used in the ordinary way. The following illustrates the calculation of a PSF that uses the field-dependent model"
]
},
{
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