ABSTRACT
The air-spaced triplet is sometimes referred to as a Cooke triplet. It was developed by Harold Dennis Taylor in 1894 (he worked for a company in York, England: T. Cooke and Sons). There are enough degrees of freedom to design an anastigmat lens. Referring to Figure 3.1, for a series of three thin lenses (note that although the lenses are thin, the air spaces separating them are appreciable), the Petzval sum, longitudinal chromatic, and lateral color are set to zero as system power is controlled. Assume that the materials for the first and third lenses are the same that the stop is at the second lens, and a distant object. Triplet lens. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/fig3_1.tif"/>
F a = 1/P a, where P a is the power of the first lens, etc.
TR = T 2/T 1
() T 3 = [ ( F a − T 1 ) F b − ( F a + F b − T 1 ) T 2 ] F c ( F a − T 1 ) F b + ( F a + F b − T 1 ) ( F c − T 2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq78.tif"/>
X = T 3 PTR, where P is the power of the lens assembly
() P b = 1 F b = − P c N b X + 1 N a https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq79.tif"/>
() P a = X P c https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq80.tif"/>
() P = P a + P b + P c − T 1 P a ( P b + P c ) − T 2 P c ( P a + P b ) + T 1 T 2 P a P b P c https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq81.tif"/>
() P c = 1 / X − [ ( X / T R 2 + 1 ) V b N a / ( V b N a / ( V a X N b ( X + 1 ) ) ) ] T 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq82.tif"/>
