The SELFOC Lens Array is used in 1:1 image transfer applications. The arrays are composed of one or more rows of lenses. The images from adjacent lenses overlap and form a continuous erect image. The SLA’s short total conjugate (TC), ranging from 9 to 80 mm, allows the designer to decrease the optical path length and, thus, reduce the overall size of the system.
|SELFOC® Lens Array (SLA) – Technical Charts
Table 1 Paper Size and Dimensions (mm)
Table 2 Optical Parameters & Performance of SLA
* DOF is based on 10% MTF @ 6LP/mm and is for reference only, not inspected.
** Consult SELFOC® Lens Array Reference Book for complete design and application data.
SELFOC® MicroLens – Instructions
Key to optical parameters: (all units in millimeters unless otherwise stated)
λ Wavelength of incident light in microns (>0.55 mm)
L1 Object distance (from object point to lens’ front surface)
L2 Image distance (from lens’ back surface to image point)
N0 On-axis refractive index of SELFOC® lens
√A Index gradient constant (mm-1)
Z Lens length
EFL Effective focal length (from rear primary plane to rear focal plane)
BFL Back focal length (from rear lens surface to rear focal plane)
MT Transverse magnification
θ+ Maximum angle from object above axis
θ- Maximum angle from object below axis
Hm Maximum object height
Ls Distance from lens surface to aperture stop
Steps for using the SELFOC® MICROLENS Tables:
- If the object distance for your application is known, click the sheet tab entitled “Obj. Distance”. If the desired magnification is known, click the sheet tab entitled “Magnification”.
- Enter the required data in the colored data cells. As you enter numeric values, the SELFOC® lens parameters such as N0, √A, and EFL will be recalculated in the lens table.
- Adjust the Pitch in small increments and observe how the optical parameters are altered. Recall that 2πP=Z√A.
Recommended Storage and Handling of Lenses
For extended periods of time, the lenses should be stored in a “dry box” environment (40%RH or less). This entails the use of a desiccant (e.g., silica gel) or a heat source to prevent humidity from leaching the lens material. This is much more critical for non-coated lenses, since AR coatings help to protect the lens surfaces from humidity. For short term storage (less than a month), the plastic box and foam packing in which the lenses are shipped will provide adequate storage.
In addition to humidity requirement, the lenses need to have sufficient spacing to avoid potential damage such as chipping and scratching from other lenses. For this reason, Go!Foton storage boxes have built-in slots in which the lenses are placed, with surrounding packaging to hold them securely in place.
After opening the lens boxes, it is important to exercise extra care in lifting the plastic shield. Particularly with smaller lenses, it is possible that they may cling to the shield and be lost during removal. Lenses should be handled with plastic tweezers, preferably those with a tapered end. Lenses should be picked up out of their individual compartments by firmly holding each by its side surface (not the ends).
At times it is necessary to clean the lens surfaces due to the presence of some dust or film which may impair the image. Go!Foton generally recommends the use of ethyl alcohol as a cleaning solvent. Acetone may also be used, without harm to the lens, but it should be pure enough to no leave a residue on the lens’ surface.
Physics of SELFOC
The Gradient Constant
The SELFOC lens utilizes a radial index gradient. The index of refraction is highest in the center of the lens and decreases with radial distance from the axis. The following equation describes the refractive index distribution of a SELFOC lens:
N(r) = N0(1 – √A2/ 2 * r2)
This equation shows that the index falls quadratically as a function of radial distance. The resulting parabolic index distribution has a steepness that is determined by the value of the gradient constant, √A. Although the value of this parameter must be determined through indirect measurement techniques, it is a characterization of the lens’ optical performance. How rapidly rays will converge to a point for any particular wavelength depends on the gradient constant. The dependence of √A and N0, on wavelength is described by the dispersion equations listed at the end of this product guide. Note that different dispersion equations apply to different lens diameters and numerical apertures.
Lens Length & Pitch
In a SELFOC lens, rays follow sinusoidal paths until reaching the back surface of the lens. A light ray that has traversed one pitch has traversed one cycle of the sinusoidal wave that characterizes that lens. Viewed in this way, the pitch is the spatial frequency of the ray trajectory.
The above equation relates the pitch (P) to the mechanical length of the lens (Z) and the gradient constant. The figure below illustrates different ray trajectories for lenses of various pitch. Notice how an image may be formed on the back surface of the lens if the pitch is chosen appropriately.
In contrast to the optics of homogeneous materials, gradient-index optics involve smoothly-varying ray trajectories within the GRIN media. The paraxial (first-order) behavior of these materials is modeled by assuming sinusoidal ray paths within the lens and by allowing the quadratic term in Equation 1 to vanish in the ray-tracing calculations. All of the usual paraxial quantities may be calculated with the help of the ray-trace matrices given at the end of this product guide. The formulae for common paraxial distances have also been tabulated for quick reference.