# Optical Diffraction Tomography Using Nearly In-Line Holography with a Broadband LED Source
## 3 Experimental Setup and 3D RI Reconstructions  
The experimental setup used in our experiments combined a standard bright field microscope (AmScope T490B-DK 40X-2000X, Irvine, CA, USA) in which an LED ring illumination unit (Adafruit, ID: 1586, 24 LED pixels, bandwidth = 20 nm, New York, NY, USA) replaced the bright-field illumination unit incorporated with the commercial microscope. The experimental setup is shown in Figure 3. The LED ring had a radius of approximately 30 mm. To assume plane-wave illumination, the LED was placed far enough from the sample (at a distance around 35 mm) so that the wavefront illuminating the sample was flat enough. For imaging, an objective lens of magnification 40\(\times\) and \(NA\) of 0.65 was used (Plan Achro, part of the AmScope system). Images were captured using a scientific color CMOS camera (Thorlabs Zelux, resolution: 1440 \(\times\) 1080, pixel size: 3.45 \(\mu\)m, Bergkirchen, Germany). The LED ring was driven using an Arduino kit (Arduino Uno). For proper synchronization, a Matlab script was used to synchronize the LED ring with the camera for different illumination angles. Each image took 0.5 s to be acquired with a total of 12 s for the acquisition of the 24 images. Using more powerful LEDs or laser diodes can result in shorter acquisition speed. While an LED source was used in this study, the described technique is also applicable to laser sources. The advantage of using LED is to get rid of speckle noise usually seen with high coherent illumination, and they are practically advantageous (low cost angle scanning by sequential LED illumination). The center of the LED ring was aligned with the optical axis as described in the previous section. As we will show later, any misalignment will severely affect the quality of the reconstruction. In addition, the illumination and imaging \(NA\)s were matched by controlling the distance between the sample and the LED ring to ensure proper extraction of the \"Principal\" field only from the intensity measurement. As shown in Figure 3b, the distance (\(h\)) was controlled so that the illumination and imaging \(NA\) were perfectly matched. In other words, the distance (\(h\)) should satisfy the following condition:  
\[\sin\gamma=\frac{r}{\sqrt{r^{2}+h^{2}}}=NA_{OBJ} \tag{9}\]  
Figure 4 shows an example for a raw image taken for a cheek cell extracted from human mouth. Figure 4b shows the two circles (i.e., cross terms) as expected from the theory. As explained in the previous section, by carefully aligning the LED ring to match the imaging \(NA\), we were able to completely decouple the two cross terms for proper reconstruction of the 3D RI distribution. Figure 4: Intensity raw image from the experimental setup (**a**) 2D intensity image for human cheek cell. (**b**) 2D Fourier transform of the image shown in (**a**). Figure 3: Experimental setup. (**a**) bright-field microscope equipped with an LED ring. (**b**) Schematic of the system with its different parts. (OBJ: objective lens, L: lens, det. : detector). The LED ring is perfectly aligned with the optical axis for better quality of the reconstruction. The distance (\(h\)) is controlled to ensure a perfect match between the illumination and imaging \(NA\). We refer to the raw intensity images as holograms, since holography is generally referred to an image where the amplitude and phase can be extracted as was first described by [PERSON] in which the recorded image on the film has information about the complex field of the transparent sample being imaged. In [PERSON]'s original work the reference beam was propagating in the same direction as the signal beam; therefore, it was difficult to separate one from the other. The work of [PERSON] and [PERSON] placed the reference beam at a sufficiently large angle that the reconstructed signal beam was separated in the Fourier space from the Zero-order beam.