## 4 Imaging System Characterization and Performance
### Optical Resolution and Depth of Field  
One of the most important parameters in microscopy is the effective spatial resolution of the system, or how small a feature the device can reliably detect and quantify. Several metrics and methods have been proposed to assess image resolution [18]. The Rayleigh diffraction limit, given earlier in the manuscript (c.f. Section 2), provides theoretical information about the absolute spatial resolution limit of the system. It represents the resolution limit a properly setup imaging system can achieve according to its specifications, namely, the numerical aperture and illumination wavelength [18]. The modulation transfer function (MTF) of a system is metric available to estimate its optical resolution from a practical standpoint. The MTF is a representation of the modulation frequencies that can be resolved by an optical system in the Fourier (frequency) domain. As commented above, the MTF profile of a properly setup microscope system should coincide with the Rayleigh resolution limit approaching zero modulation. We used two methods to evaluate the MTF: The USAF-1951 resolution chart and the knife-edge methods [23]. Both the distribution, in terms of the diffuse angular properties, and the wavelength of the illumination affect optical resolution [22] are two competing parameters when assessing the resolution performance of the LED and VCSEL illumination systems used in this work. The MTF resolution results for both LED and VCSEL illumination are reported in Figure 7.  
The modulation transfer function results of Figure 7 show that the intensity contrast decreases as expected from full modulation to below 20% contrast at \(\sim\)120 cyc/mm. Half modulation is achieved at spatial frequencies near 70 cyc/mm. The results from the knife edge method or the USAF-1951 resolution chart are very similar for both the LED and VCSEL-based illumination systems, meaning that the differences from a practical resolution performance standpoint should be minimal. Considering the differences in wavelength, one would expect higher resolution benefits in favor of the LED illumination configuration. This means that, although the imaging system is indeed diffraction-limited for the VCSEL illumination, the sensor-driven Nyquist frequency limit effectively reduces the resolution performance of the imaging system when LED lighting is employed. Another aspect mentioned above is the impact of diffuse lighting on resolution. Although the diffuse aspect of the illumination distribution, important with the LED system, has been shown to negatively affect resolution, it has not been thoroughly quantified [22]. More work is needed in this area to fully optimize a microscope imaging system when diffuse lighting is used. We remind the reader that diffuse lighting is employed in applications where obscuration or other aspects may compromise image quality at the probe volume, such as dense particle fields, high pressure and temperature environments, or long working distances. The resolution performance results indicate that the microscope imaging system should be able to resolve features as small as 4 to 5 \(\upmu\)m. To provide more information about the system's capabilities to detect and quantify small drops or particles, we imaged calibrated opaque disks of various diameters printed on a transparent glass substrate. The printed face of the substrate was located at the object plane and the images with the opaque disks were analyzed to extract equivalent diameter [23]. Figure 8 presents a comparison between measured and calibrated disk diameters when illuminating the scene with both the LED and VCSEL systems. We imaged disks ranging from 2 to 100 \(\upmu\)m, but disks below 4 \(\upmu\)m were not reliably detected by the system. This is in agreement with the findings of Figure 7. It is important to note that despite being detected and measured, the 4-\(\upmu\)m disk's measured diameter deviated from the calibrated size by more than 20% (4.9 \(\upmu\)m).