## 2 A gradient Index Plate in a Multispectral Camera  
### Multispectral Camera  
In recent years, the ONERA laboratory has been developing ultracompact and very high-performance infrared cameras. To provide a very low noise temperature difference (so-called NETD) for the whole camera, including the IR detector and the optics, we have developed cryogenic multichannel cameras [27; 28; 29; 30]. The latest example is a multispectral camera, for which the concept is illustrated in Figure 1. It consists of an array of 2 \(\times\) 2 lenses with a focal length of 7 mm and an F-number of 4. Each channel has a field of view of 40\({}^{\circ}\)\(\times\) 30\({}^{\circ}\) and forms a 320 \(\times\) 256 pixel image on each quarter of the detector. An array of 2 \(\times\) 2 filters is placed after the lens array, so that each optical channel corresponds to a different spectral band with a width of about 200 nm. Cooling the lens array and the filters allows a very low instrumental flux to be obtained. This multispectral camera has a NETD close to that of the IR detector itself to ensure high performance levels. This kind of camera can be used, for example, in the field of gas leak detection and quantification in industrial installations.  
The optical system is thus composed of only two optical objects, a lens array for imaging and a filter array to select a specific spectral band for each channel. These components are integrated into the cold shield of a Detector Dewar Cooler Assembly (DDCA) and are cooled to cryogenic temperature. The drawback of adding optical components inside the DDCA is that it increases the thermal mass of the cold shield and this tends to increase the cool-down time of the DDCA. In order to limit the additional mass to be cooled, we wanted to remove one of the components. The filter array is made of interference filters composed of multiple thin layers deposited on a substrate. It is challenging to deposit these films on a nonplanar surface such as the lens array. Consequently, a viable solution would be to use a GRIN optic to integrate both focusing and filtering functions in the same flat and thin glass plate, achieving the expected mass reduction. In this work, we studied only one channel of this multichannel camera.  
A GRIN focusing plate needs radial index variation to create optical power instead of a spherical surface. A classical index profile used in this case is described in Equation (1):  
\[\mathrm{n}(\mathrm{r})=\mathrm{n}_{0}+\mathrm{n}_{\mathrm{r}}\mathrm{r}^{2} \tag{1}\]  
where \(\mathrm{n}_{0}\) is the refractive index on the optical axis, \(\mathrm{r}\) the radial position and \(\mathrm{n}_{\mathrm{r}}\) the coefficient of index variation. This refractive index distribution gives to the optical plate an optical power V [31]:  
\[\mathrm{V}=\frac{1}{\mathrm{f}}=-2\mathrm{n}_{\mathrm{r}}\mathrm{t}=-\frac{ \Delta\mathrm{n}}{\mathrm{R}^{2}}\mathrm{t} \tag{2}\]  
where f is the focal length, t the thickness of the plate, \(\Delta\mathrm{n}\) the refractive index variation and R the half-diameter of the lens. The issue with such a refractive index profile is achieving a short focal length (i.e., a huge V value). Since V is proportional to the index variation (Equation (2)), a short focal length as the focal length of the studied camera requires a large \(\Delta\mathrm{n}\) value. For a 7 mm focal length like in our situation, this type of design needs a gradient index with a maximum variation of \(\Delta\mathrm{n}=0.11\) for a thickness of 1 mm. This is higher than what has been achieved previously with a femtosecond laser [15]. One of the highest index variations reached to date in mid-IR glasses and with FLDW was about 0.05 in As\({}_{2}\)S\({}_{3}\) (a chalcogenide glass) [32].  
Figure 1: Cross-section of the ONERA multispectral camera. The diaphragm, the lens array, the filter array and the sensor are shown from top to bottom.