A New Method to Retrieve the Three-Dimensional Refractive Index and Specimen Size Using the Transport Intensity Equation, Taking Diffraction into Account

Abstract

Refractive index retrieval is possible using the transport intensity equation (TIE), which presents advantages over interferometric techniques. The TIE method is valid only for paraxial ray assumptions. However, diffraction can nullify these TIE model assumptions. Therefore, the refractive index is problematic for reconstruction in three-dimensions (3D) using a set of defocused images, as diffraction effects become prominent. We propose a method to recover the 3D refractive index by combining TIE and deconvolution. A brightfield (BF) microscope was then constructed to apply the proposed technique. A microsphere was used as a sample with well-known properties. The deconvolution of the BF-images of the sample using the microscope’s 3D point spread function led to significantly reduced diffraction effects. TIE was then applied for each set of three images. Applying TIE without taking into account diffraction failed to reconstruct the 3D refractive index. Taking diffraction into account, the refractive index of the sample was clearly recovered, and the sectioning effect of the microsphere was highlighted, leading to a determination of its size. This work is of great significance in improving the 3D reconstruction of the refractive index using the TIE method.

Malaria-Infected Red Blood Cell Analysis through Optical and Biochemical Parameters Using the Transport of Intensity Equation and the Microscope’s Optical Properties

“…In the presence of pure phase objects such as RBCs at the wavelength λ = 800 nm, the brightfield image essentially reduces to Equation (2), making it possible to perform linear deconvolution [21,22]:bold-italici=bold-italico⊗PSF+bold-italicN…”

“…In this study, we first used deconvolution to subtract the contribution of out-of-focus planes and distortions due to the image acquisition system set-up from the images. This made it possible to preserve the TIE paraxial ray assumptions where the diffraction would be prominent [22]. In this approach, an appropriate model of a PSF reflecting the properties of the image acquisition system set-up was required for a deconvolution that would remove diffraction effects and any artefacts.…”

“…Indirectly accessible parameters were refractive index nc of air at the time of the measurement and the depth zp of the point object in the specimen layer. These were computed by following the approach of Agnero et al [22]. n c was determined using Equation (3) [25,26]:nc=1+(6.4328·10−5+2.94981·10−2146−λ−2+2.554·10−441−λ−2)15·PT where T and P represent, respectively, the temperature in degrees Celsius and pressure in bar at the time of image acquisition, λ is in μm.…”

“…The model of Gibson and Lanni [23] is an accurate model for PSF generation that is suitable for brightfield imaging [22]. It was applied for restoration of the sample images using the Richardson–Lucy algorithm [27,28] with the number of iterations set to 30.…”

Development of a multispectral microscopy platform using laser diode illumination for effective and automatic label-free Plasmodium falciparum detection

“…The construction of this new multispectral and multimodal microscope aims to address the limitations cited above and allows investigation involving several microscope configurations such as transmission, reflection, excitation, fluorescence, polarisation, defocus, diffraction, interference and super resolution, [22][23][24] in addition to being cost-effective with the ability to evolve in space and time according to the needs of the user by adding new optical components (such as optical densities, polarisers, optical filters, new illuminations sources and optical lens) without modifying the default system path.…”