# Multi-mode Microscopic Hyperspectral Imager for the Sensing of Biological Samples
## 2 Materials and Methods  
### System Setup and Calibration  
The schematic of the microscopic hyperspectral imager is shown in Figure 1a,b. The system consists of the objective, imaging lens, slit, collimator lens, prism-grating-prism (PGP) structure, tube lens and CMOS (complementary metal oxide semiconductor) sensor. All of the optical components, with \(\mathcal{O}\)1\" (25.4 mm) diameter, were installed in aluminum tubes of SM1 thread standard. In this system, the signal emitted from the focal plane is captured by a plane achromatic 40\(\times\)/0.65 objective (RMS40X, Olympus, Tokyo, Japan), then passes through the imaging lens (f = 50 mm, DHC, Beijing, China) and converges onto a slit with 10 um width. After passing through the slit, the signal is collimated by a doublet lens (f = 50 mm, DHC, Beijing, China) and then dispersed by the PGP structure. The parameters of the grating are 300 grooves per millimeter with a 17.5 degree groove angle (GT25-03, Thorlabs, Newton, NJ, USA), and the deflection angle of the prism is 10 degree. The PGP structure is used to deflect the 1 st order diffraction pattern into the detection module. The spread spectrum is finally focused on the CMOS sensor (ASI74 MM, ZWO, Suzhou, China) through a tube lens (f = 50 mm, DHC, Beijing, China). The short and long axes of the camera were set as the spatial and spectral axes, respectively. The imager was mounted on a traditional microscopy, whose specimen holder was on an XYZ three-axis motion stage (HDS-CBMS-XYZ-I-R, HEIDSTAR, Xiamen, China). Through single push-broom scanning, a hyperspectral cube of tested sample can be obtained. Figure 1h shows the whole prototype of this system. We then performed the wavelength calibration to translate the pixel index to wavelength. A mercury lamp (HG-1 calibration source, Ocean Optics, Largo, FL, USA) was used as the standard optical source [13], whose spectrum was captured by the imager and shown in Figure 1c. There were six vertical lines in the spectral image, representing 435.833 nm, 546.074 nm, 578.013 nm, 750.387 nm, 763.511 nm and 772.376 nm light lines emitted from the mercury lamp source. The corresponding pixelindex values in the spectral axis of the CMOS were 1381, 1070, 979, 517, 483 and 459. The wavelength of the imager is assumed to be a polynomial function of the pixel index of the spectral axis:  
\[\lambda=\alpha_{0}+\alpha_{1}x+\alpha_{2}x^{2} \tag{1}\]  
where \(\lambda\) is wavelength, \(x\) is pixel index, and \(\alpha_{0},\ \alpha_{1},\alpha_{2}\) are calibration coefficients. A least squares polynomial fit method [14] is employed to investigate the relationship between the wavelength and pixel index, giving the values of the calibration coefficients as 952.9, \(-\)0.4022 and 2.017 \(\times\) 10\({}^{-5}\), respectively. The calibration result is shown in Figure 1e. After wavelength calibration, each pixel index corresponds to a specific wavelength. Figure 1d shows the spectrum of the calibration source obtained from the imager, and the full width at half maximum (FWHM) of the spectrum line of 546.074 nm is about 3 nm, suggesting the spectral resolution of our system is 3 nm. As a comparison, we also measured the spectrum of the same mercury lamp by a commercial spectrometer (PG 2000 Pro, Fuxiang, Shanghai, China), and the result is shown in Figure 1f. It is found that the wavelengths for the spectral peaks are consistent with (d), indicating the accuracy of our imager for spectral measurement. However, there exist some differences of peak intensities in several wavelength, due to the difference in the optical intensity response of the CMOS camera. Due to the aberration introduced by the diffraction module, the actual lateral spatial resolution of the imager is inferior to the theoretical calculated resolution of the microscopy (0.61\(\times\) \(\lambda\)/NA). In order to demonstrate the specific resolution of the imager, a hyperspectral imaging experiment for a resolution test target (1951 USAF-R1 DS1P, Thorlabs, Newton, NJ, USA) was performed.