使用短波通和长波通滤波片的用户自定义带通滤波

1、Custom Bandpass Filter using Shortpass and Longpass FiltersBandpass filters are optical filters that allow transmission of a specific range of wavelengths, or band, while blocking other wavelengths. Many off-the-shelf bandpass filter options are available, but when an application has specific requir

2、ements for bandwidth or center wavelength not readily available, Longpass and Shortpass filters can be stacked creating a customized bandpass filter. Longpass filters are optical filters that reflect short wavelengths while transmitting, or passing, long wavelengths. Conversely, Shortpass filters tr

3、ansmit short wavelengths but reflect long ones. Examples of both are represented in Figure 1.500nm Shortpass Filter1009080 7。目40302010 0300350400450500550600Wav&length (nm)450nm Lonjpass Filter1009080706050403020100300350400450500550600Wavelength (nm)Figure 1: Transmission Comparison of Shortpass an

4、d Longpass FiltersThe transmission graphs are very similar to Heaviside functions (denoted as H(/ ) in mathematics. As shown in Equation 1, Heaviside functions are specialized piecewise functions that have a value of one for a certain domain and zero for the rest. The domain is determined by the con

5、stant x.(Equation 1)H(/ ) can be denoted as the transmission of a filter andA as the wavelength. Figure 2 shows a Heaviside model of the LWP graph from Figure 1.1.00.80.60.40.20 3003S0HU - 450=肾400450500550600A 450世 450Figure 2: Heaviside model of the Longpass curve from Figure 1A custom optical ban

6、dpass filter can be made by using at least two filters. This is conceptually very similar to multiplying Heaviside functions in mathematics. In order to obtain a rectangular function from 540 to 545, the two Heaviside functions must be multiplied together as shown Solution 1 and Figure 3MEWS。) = ；：；

7、H2 =S。)热土 too。A 500(Solution 1)1.00.80.60.40.20300350400450500S50600Figure 3: This graph is of the rectangular function of BP】.What is achieved through multiplication in mathematics is achieved physically by layering two or more optical filters. When layering multiple optical filters, light propagat

8、es through one filter and into the next. Because each filter transmits certain wavelengths, layering allows for the transmission of a customized band of wavelengths.nnv_vUJFigure 4: A custom bandpass filter where F1 and F2 represent Longpass and Shortpass filters.This results in a transmission curve

9、 represented in Figure 5.100450 nm Longpass and 500 nm Shortpass Filters Combinedooooooooo Qz no 7 Jo CJ 4 3 2 1Stacked Fibers 450nm Longpass SOOnm Sbortpasso030oCJ300o o fo 505 450Wavelength nmFigure 5: The transmission curves of a custom bandpass filter produced by stacking a 450nm Longpass and 500nm Shortpass FilterStacking Longpass and Shortpass filters can quickly create a custom solution for selecting a specific bandpass and is an ideal alternative in scenarios where