Lens Design II Seminar 6 (Solutions)

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1 Prof. Herbert Gross Yi Zhong, Norman G. Worku Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str Jena Lens Design II Seminar 6 (Solutions) 6.1. Correction of a Ploessl eyepiece An eyepiece is a system to view a finite intermediate image with the relaxed eye. Since the human eye pupil is inside the body and a certain space is necessary to allow for the insertion of eye glasses, the pupil of the eyepiece must be located remote. This enlarges the diameter of the system and is a problem for the correction. The approach of Ploessl is in particular an eyepice with two achromatic components with the crown glasses oriented towards the inner air distance. a) Setup a Ploessl eyepiece with focal length f = 40 mm for the wavelengths dfc out of two achromates with glasses SF12 and BK7 with thicknesses 3 mm and 10 mm and equal focal power respectively. The diameter of the intermediate image is 20 mm, the chief ray path is telecentric here. The eye pupil should have a diameter of 2 mm. The two achromates are positioned in a small distance of 1 mm. b) Optimize the air distances in the system first for the basic data of pupil and focal lengths using only air distance changes. Is the pupil aberration negligible? c) Now optimize all radii for axis, zone and outer field point for an optimal performance. Is the system diffraction limited? What are the dominating residual errors? Solution: a) First a classical achromate with focal lengths f = 80 mm is established as a starting system.

2 In a second step, two achromates of these data are combined. The start value for the numerical aperture is here 2 mm / 2 / 40 mm = The object space is declared to be telecentric, the image space to be afocal. The pupil is located at the final plane. b) Now the air distances are optimized to match the pupil and the focal length as well as the eye pupil diameter.

3 The residual aberrations can be clearly seen for the outer field points. Therefore the pupil aberrations are considerable. c) In a second step, all radii are optimized. The intersection points of the chief ray and the coma rays in the eye pupil are required to be 0 / +1 / -1. The air thickness is forced to be larger than 0.1 mm and the quality is required to be best for the angle deviation.

4 The system is not diffraction limited, but very nearby. If the aberrations are investigated it is seen, that distortion (3.5%) and astigmatism (0.64 ) are th dominating residual aberrations.

5

6 6.2. F-Theta Scan Lens Scan lenses are used for moving a field point over the image area by rotating a mirror. If the image height is direct linearly depending on the mirror angle, we have the so called f-theta lenses. This is a special distortion approach to switch from a sin- to a tan-dependence of the field height. a) Establish a BK78-Lens with focal length f = 100 for the wavelength = 488 nm. To obtain a model of the scanning unit, establish a plane mirror, which deviates the ray by 90 and then in a distance of 40 mm a second mirror, which deviates the ray by -90. If now the lens has approximately a distance of 60 mm from the second mirror, the rotating first mirror lies in the front focal plane of the lens. Therefore the chief ray will be telecentric in the image space. Generate a multiconfiguration with the angles 45, 46, 47, 48 and 49 for the first mirror and optimize the radii and the image distance. b) Now add in the merit function the requirements, that the image heights increase with 3 mm per step and that the chief rays are telecentric. Remove the focal length target and optimize also the distance between the lens and the mirrors. c) No add additional lenses for the system until you obtain a diffraction limited design for all scan positions. What is the remaining telecentricity error for the final solution? Solution: a) The setup looks like this:

7 b) c) In the case of two lenses, the setup is for example as follows. The largest scan positioin is not still good in quality.

8 If we have 3 lenses, the performance is nearly sufficient:

9 The residual error of telecentricity is 0.27 mrad:

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