A unique method to design a high-throughput and high-resolution ultrathin Czerny–Turner (UTCT) spectrometer is proposed. This paper reveals an infrequent design process of spectrometers based on Coddington’s equations, which will lead us to develop a high-performance spectrometer from scratch. The spectrometer is composed of cylindrical elements except a planar grating. In the simulation design, spot radius is sub-pixel size, which means that almost all of the energy is collected by the detector. The spectral resolution is 0.4 nm at central wavelength and 0.75 nm at edge wavelength when the width of slit is chosen to be 25 μm and the groove density is 900 lines/mm.

In this study, we propose a method of evaluating the spectral resolution of crossed-asymmetric Czerny-Turner spectrometers by comparing the impact of different slit functions on the optical transfer function, and different slit widths, through simulation and experiments. The results show that, the Gaussian function is suitable for narrower slit widths, such as 25 μm, and the rectangle function or convolution of slit-scattering function with rectangle function is suitable for wider slit widths, such as 50 μm, 150 μm, and 200 μm. The proposed method can provide guidance in the evaluation of spectral resolution in the preliminary optical design process of spectrometers.

In this paper, an optical design for a hollow planar waveguide spectrometer with Czerny-Turner is proposed. To decrease the propagation loss of the spectrometer, the design strategy of designing the tangential plane and the sagittal plane separately is proposed, corresponding to resolution and energy, respectively. The Czerny–Turner optical path is designed on the tangential plane, and the sagittal design theory and method are analyzed in detail. The ray tracing results show that the resolution of the spectrometer is better than 4 nm on the tangential plane, while on the sagittal plane, the detector receives the highest energy when the detector pixel height matches the distance between the two mirrors.

An integrated direct-reading spectrometer scheme using seven concave gratings is proposed. At present, the optical design simulation has been completed, and the subsequent physical design may be carried out according to the simulation results. Ray-tracing software (Zemax) is used to divide the spectrum on the grating into seven bands, and an area array detector is used to receive the spectral signals simultaneously, which reduces the volume of the spectrometer and improves the spectral consistency. Using this method, a spectrometer covering 230–440 nm is designed, and the spectral resolution of the center wavelength corresponding to the seven grating windows of 230–260 nm, 260–290 nm, 290–320 nm, 320–350 nm, 350–380 nm, 380–410 nm, and 410–440 nm can reach 0.0974 nm, 0.0652 nm, 0.0361 nm, 0.0157 nm, 0.0838 nm, 0.0872 nm, and 0.1471 nm.