Telecentric lenses with variable working distance
Date: March 2017
Published by: www.vision-systems.com
Direct link: http://www.vision-systems.com/articles/print/volume-22/issue-3/features/telecentric-lenses-with-variable-working-distance.html
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Many measurement applications require dealing with the topics depth of field and variable working distances. Examples include package sorting, inspection of mobile phones and tablet cases, displays and PCBs, whereby magnifying lenses are moved over a long distance. Telecentric lenses with integrated focus tunable lens enable reproducible measurement of a large focus area within milliseconds without camera or object movement.
An important advantage of object-sided telecentric lenses is the fact, that the whole depth of field area can be used for an exact measurement of different object heights. Thereby, the magnification is constant but resolution is limit-ing the measurement accura-cy. The depth of field depends on magnification, aperture and required resolution. Especially magnifying lenses with high resolution have a severely restricted usable depth, since a very large aperture is need-ed for a sufficient image per-formance.
Besides the fast and flexible focusing of objects in different distances, the big advantage of integrated focus tunable lenses in telecentric lenses is a comparatively larger depth of field. The large depth of field is achieved by a z-scan, which can controlled electronically. The used focus tunable lens EL-16-40-TC from Optotune offers an adjustment range of the refractive power from -3 to +3.5 diopters. This range can be realized with a jump that takes 20 ms or a steady ramp during e.g. 100 ms. If a stack of pictures is taken, a “hyperfo-cus” or “extended depth of field (EDoF)” picture can be created by a suitable software. It can also be used to deter-mine object distances, a tech-nique called depth from focus (DFF).
Integration of the liquid lens
For integrating a liquid lens in a lens system, the optical design is crucial. The telecentricity principle describes that the aperture stop has to be pro-jected to infinity on the tele-centric side. Accordingly, the focus tunable lens has to be placed behind the aperture for object sided telecentric lenses. For this reason, a bi-telecentric lens with focus tunable lens is not possible. The following design require-ments can be set for telecen-tric lenses:
- Large focus range
- Low, linear change of magnification over this range
- Constant image perfor-mance
- Low change of distortion
- Constant telecentric error
To enable this system for a wide range of users, the first step was to integrate the liquid lens in an existing lens design. As a specialist for small-batch production and custom specific solutions, Sill Optics also offers individual optical designs with focus tunable lenses.
In the following, nominal de-sign, performance and meas-ured results are shown for a 2x magnifying telecentric lens and a 1” sensor.
Picture 1: telecentric lens Correctal T/2.0 from Sill Optics with integrated focus tunable lens EL-16-40-TC from Optotune Switzerland
Performance according to simulation
Design parameters are shown below with regard to the zero position of the focus tunable lens:
- Magnification: 2.0x +/- 1 %
- Working distance: 106.2 mm +/- 2 %
- Object size: 19.2 mm x 25.6 mm for sensor size 9.6 mm x 12.8 mm (1” sensor)
- Wavelength range: 450 – 700 nm
- Object sided NA: 0.04 at middle size aperture
- Theoretical max. distor-tion 0.61 %
- Theoretical max. telecen-tric error 0.01°
In standard configuration (fixed focusing), the lens has a depth of field of 0.3 mm for a pixel size of 7 µm and NA of 0.04.
The change of refractive pow-er of the tunable lens EL-16-40-TC from -3.0 to +3.5 diop-ters increases the optimum working distance from 111.5 mm to 99.4 mm. Accord-ingly, a maximum z-range of about 12 mm is possible which results in a 40 times higher DOF.
Because of the affected focal length, the magnification changes over the focus range. Change of magnification is +/- 3 % comparedto the nominal value and shows a linear de-pendence from the refractive power. This influence to the measurement results can be eliminated by calibrating the measurement system.
Imaging performance is nearly constant over the whole focus area. Changing focal length or changing working distance at constant NA, varies the diffrac-tion limit slightly. For a shorter working distance (+3.0 dpt), the diffraction limit is slightly higher. MTF plots are calculat-ed with NA = 0.04 and show an almost homogenous image quality.
Distortion of the telecentric lens stays the same type (posi-tive, pincushion distortion) and varies linearly from 0.73 % (-3 dpt) to 0.47 % (+3.5 dpt) through the whole focus range. The measurement in-fluence can also be eliminated by calibration measurements at different distances.
By definition, telecentric error remains constant, because it doesn’t depend on the sys-tem’s working distance or focal length and the front part of the lens stays the same.
Measurements confirm the simulation
The measurement of the first lens series shows an approxi-mately nominal performance. In zero position, the measured focus tunable lens shows the following properties:
- magnification: 1.983x
- working distance: 105.70 mm
- max. distortion: 0.97%
- max. telecentric error: 0.05°
The measurements show a z-range of approximately 13 mm (+6 mm / -7,2 mm). Linearity of working distance and magnifi-cation can also be confirmed in practice. Additionally, the magnification shows a low deviation (+2.6 % / -3.2 %).
Distortion over the whole fo-cus area is below 1 % and tele-centric error below 0.1 %.
The imaging quality is deter-mined with the MTF-Master on a monochrome sensor and with white illumination. As usual in practice, the best ap-erture is chosen by manual adjustment. Thus, it’s possible that the maximum values are higher than the theoretical values for NA 0.04. The MTF results confirm a good imaging performance even in the field edges.
Hereby, the influence of the shorter focal length becomes apparent. For shorter focal length, a slightly higher resolu-tion with constant aperture is achieved.
In conclusion, the lens achieves good imaging proper-ties over a z-range of approxi-mately 13 mm. Magnification and working distance show an almost linear dependence on refractive power. With calibra-tion measurements, a reliable and highly precise result can be achieved
The design data describes the system parameters reliably, so that future developments can be planned. Thus, wide appli-cation fields open up for tele-centric measurement systems.
