## 2 Microscope Imaging Apparatus
### Ultra-Fast Illumination Solutions
#### 2.1.1 High-Power Light-Emitting Diode Illumination Source  
We have developed various high-current electronics for our LED system, increasing or tuning their performance with each generation. The latest driver was developed for a quad-channel multi-die LED emitter, which demonstrated exceptional bandwidth at very high radiation power. This four-channel driver can generate short pulses at current levels above 220 A. It demonstrated extreme stability, short pulse capability below 10 ns, and repetition rates well above 5 MHz, a major improvement compared to all commercially available systems. In this work, we coupled the driver with a custom-made royal blue, quad-channel, multi-die LED emitter (custom LEDengin LZP). The customization of this LED emitter includes the selected wavelength of the emission spectrum (centered at 457 nm, with a 22-nm bandwidth), as well as the replacement of the LED glass dome for a flat glass window, which contributes to the simplicity and flexibility of the optical set-up to maximize light collection and transmission. Blue and UV LED emitters generally present the highest flux of all LED chips; they rely on a gallium nitride (GaN) semiconductor to form a p-n junction by silicon and magnesium doping, and convert the electric energy into photons of short wavelength, due to the high energy bandgap of GaN. Indium nitride (InN) is typically added to GaN to change the energy bandgap and tune the dominant radiation wavelength of the LED.  
The high dispersion of typical LED output radiation (120\({}^{\circ}\) for the emitter used in this work) results in rapidly decreasing energy density on and off axis with distance. Specific optics need to be used to collect and transmit the LED output light with the minimum amount of energy loss. To keep the configuration simple in this work, we used a single 16-mm focal length aspheric condenser lens located just under 10 mm away from the LED emitter's glass window. Figure 2 presents a ray tracing simulation of the optical arrangement, with the LED emitter located on the far left of the diagram, and the light rays represented in purple color. The measurement volume is represented in red, at 80 mm from the LED emitter, with the middle of the measurement volume corresponding to the object plane. The condenser lens is shown in dark gray and the effective collection space of the long-distance microscope objective is shown by a dark gray rectangle.  
The ray tracing simulations of Figure 2 show the good behavior and coherence of the wavefront, as indicated by the unidirectional trajectories of the rays, which is important for line-of-sight imaging. This configuration represents a factor nine improvement over the bare LED emitter at this location, according to the ray tracing simulation results. Nevertheless, a large fraction of the LED output radiation does not illuminate the probe volume, with nearly over a 99% loss. These simple simulations do not account for the energy distribution of the LED emitter, but only represent the radiation over the full width at half maximum angle, per the LED specifications (120\({}^{\circ}\)). More accurate energy figures are provided later in this manuscript along with a full characterization of the LED radiation output.  
Figure 2: Ray tracing simulation showing the output radiation of the light-emitting diode (LED) emitter on the left. The LED output is collected and transmitted by a 16 mm focal length condenser lens. The probe volume is shown in red and the microscope objective’s effective collection is represented by a dark gray rectangle.