# Using Tube Lenses with Infinity Corrected Objectives

This is **Section 9.2** of the Imaging Resource Guide.

In order to create an image with an infinity-corrected objective, a tube lens must be used to focus the image. One advantage to using an infinity-corrected objective with a tube lens is that there can be a space between the objective and tube lens. The space allows additional optical components to be inserted into the system, such as optical filters or beamsplitters. The distance between an infinity-corrected objective and the tube lens (L) can be varied from the recommended or optimal, but this will affect the image field diameter ($ \varnothing $). Equations 1 and 2 are approximation formulas to determine the relation between ($ \varnothing $) and L.

**(1)**$$ \varnothing_1 =2 \times f_1 \times \text{NA} $$

**(1)**

where $ \small{\varnothing _1} $ is exit pupil of the objective, $ \small{f_1} $ is focal length of the objective, and NA is the numerical aperture of the objective.

**(2)**$$ L = \frac{ \left( \varnothing_2 - \varnothing_1 \right) \times f_2 }{\varnothing} $$

**(2)**

Where L is the distance between the objective and the tube lens, $ \small{\varnothing _2} $ is entrance pupil of the tube lens, $ \small{f_2} $ is focal length of the tube lens, and $ \small{\varnothing } $ is the image field diameter.

## Application Example:

Using an M Plan APO 10X objective (#46-144), MT-1 tube lens (#54-774), and a 2/3” sensor camera, what is the maximum spacing between the tube lens and objective without vignetting? The focal length of the objective ($ \small{f_1} $) is 20mm and NA is 0.28, so the exit pupil diameter can be calculated:

**(3)**$$ \varnothing_1 = 2 \times 20 \text{mm} \times 0.28 = 11.2 \text{mm} $$

**(3)**

A 2/3” image sensor features an 11mm diagonal, therefore $ \varnothing $ needs to be at least 11mm. The focal length of the MT-1 tube lens is 200mm and the entrance pupil diameter is 24mm. Therefore,

**(4)**$$ L = \frac{ \left( 24 \text{mm} - 11.2 \text{mm} \right) \times 200 \text{mm} }{11 \text{mm}} = 232.7 \text{mm}$$

**(4)**

As long as the spacing between the tube lens and objective is less than 232.7mm, there will be no vignetting.

*Application Note*

*Application Note*

*Application Note*

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