Fourier Multispectral Filters

Light spectrum (or spectrometry) is used in many applications ranging from medical, agriculture, security and encryption. For example, food safety can be determined by examining the spectral content of food and comparing it to a known standard. Information can be encrypted into the spectrum and used in security application. This can also be extended to imaging applications. Instead of the traditional discrete RGB colors, it is possible to acquire a continuous spectrum at each pixel, producing a three-dimensional cube of information (2D spatial and 1D spectral).

Currently used techniques include hyperspectral and multispectral imaging. Hyperspectral imagers utilize a moving diffraction grating to disperse the light. These are often bulky systems. Multispectral imagers utilize a large number of narrow band filters on each pixel to approximate a spectral continuum. However, this has to be application-specific; i.e., the narrow band filters have to be designed to match the expected spectral peaks of the target. Additionally, narrow band filters discard most of the signal leading to a low signal to noise ratio.

Our approach to multispectral sensing uses a fundamentally different approach, called Fourier filtering. These are filters with a sinusoidally shaped transmission as a function of frequency (or wavenumber). By taking several measurements using sinusoidal filters with different periods(at different pixels), it is possible to reconstruct the original spectrum. The advantage compared to narrow band multispectral sensors is that we do not need prior knowledge of the spectrum. Additionally, these filters are broad band, so most of the light is used in the reconstruction, resulting in a higher signal-to-noise ratio.

Array of Fourier Spectral FIlter Pixels fabricated using ZnS on a glass substrate

Filter array attached to a commercial image sensor

Reconstructed spectra of LED targets. GT=Ground Truth


  1. Chuan Ni, Jie Jia, Matthew Howard, Keigo Hirakawa, and Andrew Sarangan. “Single-shot multispectral imager using spatially multiplexed fourier spectral filters”. J. Opt. Soc. Am. B, 35(5):1072–1079, 2018. doi:10.1364/JOSAB.35.001072
  2. Jie Jia, Chuan Ni, Andrew Sarangan, and Keigo Hirakawa. “Fourier multispectral imaging”.
    Optics Express, 23(17):22649, 2015. doi:10.1364/OE.23.022649
  3. C. Ni, J. Jia, K. Hirakawa, and A. Sarangan. “A Fourier multispectral imaging camera with pixel-level sinusoidal filter arrays”. 2016 IEEE Photonics Conference, IPC 2016, 2017. doi:10.1109/IPCon.2016.7831060
  4. Chuan Ni, Jie Jia, Keigo Hirakawa, and Andrew Sarangan. “Design and fabrication of sinusoidal spectral filters for multispectral imaging”. Proc. SPIE – The International Society for Optical Engineering, volume 9556, page 95560I, 2015. doi:10.1117/12.2188830