Hi, I need an optical encoder for angle measurement of pendulum. However, I cant determine which one I should use . Can you suggest any optical encoder for me?

I will measure theta angle as shown here: http://www.mathworks.com/cmsimages/64210_wl_91891v00_uofarizona_fig2_wl.jpg

 

How do you intend to process or what nature of signal do you need? Optical encoder method usually uses the sin/cos signal of two outputs in quadrature.
It can also be done with a resolver in a similar fashion, http://www.analog.com/media/en/technical-documentation/application-notes/394309286AN263.pdf
Both items can be found on the surplus market.
Max.