THORLABS Redstone OSA305 - Apodization Functions

Optical Spectrum Analyzers Chapter 14: Appendix
Page 45 STN053070-D02
14.2. Apodization Functions
The following apodization functions are implemented in the ThorSpectra software:
Norton-Beer
(Weak)
𝐹
󰇛
𝑥

󰇜
0.384093  0.087577
󰇛
1𝑥


󰇜
 0.703484
󰇛
1𝑥


󰇜

Norton-Beer
(Medium)
𝐹
󰇛
𝑥

󰇜
0.152442  0.136176
󰇛
1𝑥


󰇜
 0.983734
󰇛
1𝑥


󰇜

Norton-Beer
(Strong)
𝐹
󰇛
𝑥

󰇜
0.045335  0.554883
󰇛
1𝑥


󰇜

 0.399782
󰇛
1𝑥


󰇜

Triangular
𝐹
󰇛
𝑥

󰇜
1𝑎𝑏𝑠󰇛𝑥

󰇜
Cosine
𝐹
󰇛
𝑛
󰇜
sin
󰇡
𝜋𝑛
𝐿1
󰇢
Hann
𝐹
󰇛
𝑛
󰇜

1
2

1cos

2𝜋𝑛
𝐿1

2-Pass Hann
𝐹
󰇛
𝑛
󰇜

1
4

1cos

2𝜋𝑛
𝐿1


Hamming
𝐹
󰇛
𝑛
󰇜
0.54  0.46 cos

2𝜋𝑛
𝐿1

3-Term
Blackman-
Harris
𝐹
󰇛
𝑛
󰇜
0.4243801 0.4973406cos

2𝜋𝑛
𝐿1


0.0782793 cos

4𝜋𝑛
𝐿1

4-Term
Blackman-
Harris
𝐹
󰇛
𝑛
󰇜
0.35875 0.48829 cos

2𝜋𝑛
𝐿1


0.14128cos

4𝜋𝑛
𝐿1

0.01168 cos

6𝜋𝑛
𝐿1

Gaussian
𝐹
󰇛
𝑥

󰇜
𝑒𝑥𝑝
󰇧

𝑥


20.4

󰇨
In these functions, 𝐿 denotes the length of the interferogram, 𝑛 is the index count (from 0 to 𝐿1), and 𝑥


󰇡


1
󰇢
.