# Compact Spectral Encoding Microscopy by Terrace Grating Optics

## TL;DR

This paper introduces a new type of 3D-printed optical component called Terrace gratings that enable continuous spectral encoding in microscopes without complex setups.

## Contribution

The novel Terrace grating optics provide continuous spectral encoding as a plug-and-play add-on for standard microscopes.

## Key findings

- Terrace gratings preserve illumination path and integrate easily with other phase masks in widefield microscopy.
- Dual-order Terrace gratings enable robust color decoding with a wavelength-independent reference spot.
- The design allows snapshot decoding of multiple colors and simultaneous depth and color readout via PSF shape.

## Abstract

Spectral information is essential in microscopy, yet
many multispectral
imaging solutions require increased optical complexity or restrict
the spectrum to a few discrete bands. In this work we introduce the
Terrace grating optics family: flat, 3D-printable elements that provide
continuous spectral encoding, as a plug-and-play add-on component
to standard microscopes. The Terrace design preserves the illumination
path in widefield operation and integrates trivially with other microscopy
phase masks. We introduce two variants: a Single-order Terrace that
concentrates energy into one diffraction order for high signal-to-noise
ratio, and a Dual-order Terrace that adds a wavelength-independent
reference spot, enabling robust color decoding. Using a Fourier-optics
model, we show that the wavelength displacement is linearly controlled
by the Terrace step-width and refractive-index mismatch. We validate
the approach in two settings: snapshot decoding of four-color mRNA
barcodes and multicolor NeuroPAL worm imaging with a single camera
exposure and instantaneous color readout. Furthermore, we demonstrate
continuous spectral and depth encoding masks yielding simultaneous
depth and color readout via PSF shape, which remains compact and
efficient. Terrace gratings thus offer a practical alternative to
prisms and blazed gratings, enabling continuous multispectral encoding
and straightforward integration with conventional microscopes.