Low-cost, open-access refractive index mapping of algal cells using the transport of intensity equation

Abstract

Phase contrast microscopy allows stain free imaging of transparent biological samples. One technique, using the transport of intensity equation (TIE), can be performed without dedicated hardware by simply processing pairs of images taken at known spacings within the sample. The resulting TIE images are quantitative phase maps of unstained biological samples. Therefore, spatially resolved refractive index information can also be determined.Using low-cost, open-source hardware, we applied the TIE to living algal cells to measure their refractive index. We obtained refractive index values that were repeatable within species and differed by distinct amounts depending on the species being measured. We suggest TIE imaging as a method of discrimination between different algal species and, potentially, non-biological materials, based on refractive index. Potential applications in biogeochemical modelling and climate sciences are suggested.

Flat-Field and Colour Correction for the Raspberry Pi Camera Module

“…Popular and well-documented APIs exist in C and Python [12] to control the camera, and there is a strong community of users working with it. There are a wide range of microscopy projects making use of the Raspberry Pi camera including the OpenFlexure Microscope [21], FlyPi [14], a fluorescence imaging system [15], and various others [8,18,9,13]. There have been efforts made in the past to correct the camera for uniform, flat-field response [17].…”

Low-cost, open-access quantitative phase imaging of algal cells using the transport of intensity equation

“…Figure 2d-f shows equivalent images for the Raspberry Pi laboratory-prototype. Images used to create the figures and table in this work, along with python code and example raw images are available in the repository [24]. The 'shadow' effect observed in both sets of images is thought to be aberration owing to slight misalignment of the incident illumination and is more pronounced when using the Raspberry Pi camera (figure 2d-f ) compared to the IDS camera (figure 2a-c).…”

“…The limiting factor on the accuracy of the TIE, and subsequent, measurements was the accuracy of the spatial offset, Δz. Complete calculation steps, along with logic to mathematically justify them, are available in the annotated python code available in the associated project repository at the DOI given in [24].…”

“…Therefore, if either of these values (thickness or object refractive index) are known, we can unambiguously determine the complementary value. (A note on the workflow is available in the repository [24].) This is not the case for some of the algal results shown below, but is useful in sizing particles of known refractive index (such as homogeneous sediment of known origin) or identifying the refractive index of objects of well-defined size.…”

“…Image acquisition with the Raspberry Pi laboratory-prototype and the openflexure scope was carried out using python running on the Raspberry Pi 3B+. Processing of all sets of images was carried out with a python script, available in the repository [24], and IMAGEJ [27].…”