## 1 Introduction  
For the past decade, scientists have been interested in the field of Biomedical Engineering [1]. In this field, the application of imaging optics is a particularly fascinating research topic. Bio-imaging technology provides an excellent solution for acquiring high quality images. Usually, when scientists observe germs, cells, tissues and other objects by microscopes, high resolution and sufficient contrast are the primary factors which determine the microscopic image quality [2, 3]. However, in the study of biology, many analytes exceed the diffraction limit of an optical microscope in the visible light band. In order to see those small analytes, scientists modify the fluorescence modules and excite them to emit light of specific wavelengths. Accordingly, we can use conventional optical microscopes to observe nanoscale objects. As a fluorescence microscope can excite fluorescence modules and detect the emitted light, the light source of the fluorescence microscope that is used to generate fluorescent light is an essential component that must be sufficiently powerful, and which must have the correct light spectrum. Halogen lamps, or xenon arc lamps with broad band light used in commercial fluorescence microscopes [4, 5, 6, 7, 8, 9, 10], are usually employed as light sources [11]. The broad band light is used for both conventional visual observation and fluorescence excitement. Considering the energy efficiency of light excitation, we understand that only a part of all emitted light, in the specified spectrum that can be absorbed by the dye (fluorescence modules), is used in the excitation process. An amount of light from the light source is blocked by different types of optical filters which cannot ideally block all undesired light, due to fabrication defects. The leaked light will generate noise and reduce image quality. Additionally, optical filters would waste most of the lamp's energy because most light energy is outside the region of the absorption spectrum. This means that we need more powerful light sources when operating microscopes in fluorescence mode. Without such light sources, the image in the view field will become darker and blurry. If the emitted light spectrum can fit into the energy absorption dye range, we can have a brighter view field and a stronger signal. In this way, selecting a light source that has excellent luminous efficiency to achieve the goal is very important in microscopy. For the past ten years, light emitting diode (LED) techniques have been developing rapidly with a major breakthrough when the luminous efficacy exceeded the 100 Ln/W mark. The high luminous efficiency has enabled LEDs to replace the traditional lamp in many applications. In addition, LEDs have other advantages, such as excellent color performance, longer lifespan, etc. Moreover, using monochromatic LEDs is a good solution to the excitation of fluorescent molecules. To work on various types of fluorescent molecules, we can choose LEDs with a corresponding spectrum to install into the microscopes. How to design an excellent LED light source has been an important issue among researchers. [PERSON] proposed a frequency-domain fluorescence microscope using LEDs as a light source in 2001 [12]. [PERSON] incorporated this new LED technique into the Colibri illumination system in 2007 [13]. [PERSON] applied different color LEDs in fluorescence microscopes that effectively suppress the peripheral light of video-enhanced DIC in 2007 [14]. [PERSON] took low-cost and long-life span LEDs to replace more expensive mercury lamps in fluorescence microscopes to detect tuberculosis in resource-poor areas in 2008 [15]. [PERSON] introduced the use of a simple light pipe to couple the light emitted from an LED light source to a fluorescence microscope in 2008 [16]. [PERSON] et al. and [PERSON] et al. used LED light sources to detect single molecules in 2009 and 2011, respectively [17; 18].