# Filters and Spectra¶

## Filters¶

GPI has five wide band filters. Because the spectral resolutions increases toward longer wavelengths, the K band is split into two filters K1 and K2. These filters overlap for the 2.12-2.19 micron range. There is also a small overlap between Y and J for 1.12-1.14 microns.

Filter Min Wavelength Center Wavelength Max Wavelength Spectral Resolution
Y 0.95 1.05 1.14 33-38
J 1.12 1.24 1.35 30-37
H 1.50 1.65 1.79 39-51
K1 1.90 2.05 2.19 61-80
K2 2.12 2.26 2.38 63-81

The above table gives the 50% cut-on and cut-off wavelengths. The 10% cut-on and cut-off wavelengths are typically an additional 0.01 microns on either side. Spectral resolutions are stated for the delta wavelength that is Nyquist sampled by 2 detector pixels. The resolution varies across the field of view due to interactions between the dispersing prism and the chromatic behavior of the refractive collimator and camera optics in the IFS.

Filter transmission profiles are distributed as part of the GPI data pipeline, in files in the \$GPI_DRP_DIR/pipeline/config/filters subdirectory. These are vendor-provided cryogenic tests made on witness samples with identical substrate and coating produced along side the GPI IFS filters.

## Spectral Layout¶

The wavelength dispersion axis is in the Y direction in GPI raw 2D data files. Longer wavelengths are toward the bottom.

(Physically the optical plane of dispersion within the IFS is horizontal when the instrument is level on the ground, but the X and Y axes are set by detector fast and slow readout axes rather than being referenced to any given notion of ‘horizontal’ or ‘vertical’).

For a given lenslet, the pixel positions as a function of wavelength x(\lambda), y(\lambda) are given as follows:

y(\lambda) = y_0 - \frac{1}{w} (\lambda - \lambda_0) \cos \theta \\ x(\lambda) = x_0 + \frac{1}{w} (\lambda - \lambda_0) \sin \theta

where, from a measured wavelength solution calibration as produced by the data pipeline, x_0, y_0 are the starting positions of that lenslet at the reference wavelength \lambda_0, the spectral dispersion is w microns per pixel, and the spectral tilt with respect to the Y axis is \theta radians.

The spectral dispersion w is very roughly 0.017 microns/pixel. However, spectral resolution varies both across wavelengths (due to the spectral dispersion of the prism materials) and across the field of view (due to the spectral dispersion of the reimaging optics lens materials, which creates a small radial distortion which vector sums or subtracts with the prism dispersion depending on location on the detector). Spectral resolutions are highest near the ‘top’ of the detector (i.e. maximum Y axis coordinates in the detector frame).

Warning

TODO update here with better information of dispersion vs filter band. It’s not exactly constant.