OPTOPUS LENS EXAMPLES

Updated 2015.01.18

[OPTOPUS HELP]    [Doc/Dev/optics.doc See FocusCouplingConcentrator, MultiAngleLight, and DiffuseSunlightCollector]   
Lens Scripts and Naming    Purpose   
BEAM WAIST --    Mb1fL80Dw33N40    Mb1fL80Dw55N20    Mb1fL70Dw77N15    Mb2fL70Dw53
COPLANARITY --    Mb2fCoplanar    Mb2fL370Ld05    Mb2fL520Ld08N12    Mb2fL390Ld02N17    Mb2fL370Ld04N20    Mb1fL420Ld12N40    Mb1fL300Ld10N40
GENERAL MULTI-BEAM --    Mb2fL340Ld09    Mb1fL400Ld53    Mb2fL440Dw437    Mb2fL380Ld55    Mb2fL200Dw167    Mb2fL260Ld27    Mb2fL270Dw250    Mb1fL340Ld29N20                  

LENS SCRIPTS AND NAMING CONVENTIONS

Files with extension lens use the script language to define one lens configuration. Extension ops signifies a process-oriented script, i.e. that shows multiple lens configurations. Optopos doesn't make this distinction, processing any file given to it the same way.

To help further identify the content of each lens file the following naming conventions are used in constructing the name:

  1. mb/sb indicates multi-beam or single-beam. Single beam is conventional ray tracing. Multi-beam encompasses both off-axis and diffuse, since the two can use the same ray tracing of beams at multiple angles of incidence.
  2. 1f/2f indicates one- or two-face lens.
  3. Inumber tells the image number. Optional and usually the last field to disambiguate otherwise identical image file names, for example where a series of images differ only in specific lens parameters.
  4. Lanything refers to focal length.
    1. Lnumber tells absolute focal length. This is supported for completeness but the absolute length is rarely useful since each length can be produced by an infinite number of configurations.
    2. Ldnumber tells the focal length deviation, where number is the two-digit percentage of focal length deviation over absolute focal length. For an sb image, this would indicate the lens focus quality. For an mb image it tells the deviation of the foci locus, where the quality of each angle focus is usually swamped out by the much larger variation between angles.
  5. DW is delta width, the percentage change in width of the beam from the lens face (width defined by lens configuration) to some plane of interest. Mathematically this is 100 x "final" width / lens width. This is usually used with lens designs intended for multi-beam ray tracing. It is similar in concept to the paraxial beam focus quality of a normal lens. For example, Mb2fL440Dw437 demonstrates the usual parabola-like multi-beam focus locus. The focus of the 40d beam is 437% further from the lens axis than the lens width, illustrating very poor beam confinement. This doesn't mean that we have some specific purpose for this position because each beam angle has a different focus; it is just a way of distinguishing configurations using an important characteristic. Mb1fL80Dw33N40 shows a single-face lens, for which DW is 33%, i.e. it shrinks the beam width. This is possible only because the index of refraction is 4.0. In this case the plane of interest is the beam waist, which actually is a usable feature and not just a means of distinguishing between lenses.
  6. N is the index of refraction of the lens x 10. Typical would be 15 but this is usually ommitted from names. N40 index would be 4.0, that of germanium.

PURPOSE

These lenses are designed to show particular features with no loss of trace rays. This is especially important in the multi-beam containment investigation. Any lens has good containment if it drops rays from the trace, suggesting that the refractive index is irrelevant. However, we can see by stretching a lens that at the best configuration for containment that includes all rays, containment is better the higher the index.


BEAM WAIST

Mb1fL80Dw33N40

Lens Ray Trace

The 33% beam width reduction without significant reflection losses is possible only because the index of refraction is 4.0. Although this is intended as a single-face lens, the egress face is in the picture and the wide splay of rays as they exit is very informative.



Mb1fL80Dw55N20

Lens Ray Trace

Mb1fL70Dw77N15

Lens Ray Trace

Mb2fL70Dw53

Lens Ray Trace


COPLANARITY

Mb2fCoplanar

Lens Ray Trace

This has not been measured for comparison. It serves only to generally demonstrate good multi-beam focus coplanarity at the expense of fuzzy foci and no beam containment. Delta beam width is approximately 250% so there is significant overlap of adjacent cells.

Beam angle foci spacing appears linearly related to the beam angle. This is interesting and could be verified mathematically but there is no obvious use for this relationship. Off-axis focussing inherently means an infinite number of beam angles (simultaneously if diffuse or over time if static solar tracking).

With static solar tracking, athough the cells process all angles over time, at any point in time all cells see the same beam angle and don't interfere with each other. The lens cells can't be seen as unified, though. Beams that are more or less vertical will focus directly under each incident lens face but beams at angles will focus under adjacent cells. This means that whatever is done at the focal plane can't be based on the beam angle, i.e. it can't be a lens face. It could be a frustrated total internal reflection puncture of a light guide.


Mb2fL370Ld05

Lens Ray Trace

This lens trades off focus quality for improved coplanarity. It has a 5% coplanarity deviation, which is the best that can be achieved. Unlike Mb2fL380Ld55, for example, the focal lengths do not monotonically decrease as the beam angle increases but instead waver around the average focal plane. This wavering shows that the foci locus function must be of greater complexity than parabolic. While there is obviously a wide range of configurations with the locus curve opening toward the left, the right-opening range is much more limited. Mb2fL340Ld09 is at this limit. Its foci monotonically increase with increasing beam angle but just barely enough to overcome the wavering.

This lens exhibits imperfect but likely adequate focus quality and better coplanarity than any of the left-opening configurations and the range of right-opening configurations is very restricted.



Mb2fL520Ld08N12

Lens Ray Trace

This is the best configuration for coplanarity given a lens material with refractive index 1.2 instead of 1.5. The coplanarity deviation is 8%, which is only marginally worse than the best with index 1.5 but the focal length is 29% longer, masking the fact that absolute coplanarity is signficantly worse. The individual foci are sharper in this configuration but that can be used to advantage only if coplanarity is irrelevant.



Mb2fL390Ld02N17

Lens Ray Trace

This is the best configuration for coplanarity with refractive index 1.7. Its foci are as sharp as the 1.5 index lens and its coplanarity deviation is 2%, which is significantly better than the 5% of that lens.



Mb2fL370Ld04N20

Lens Ray Trace

Thie represents the best coplanarity with refractive index 2.0. Its foci are not as sharp as Mb2fL390Ld02N17 and its coplanarity deviation is 4%.



Mb1fL420Ld12N40

Lens Ray Trace

This is the best beam containment acheivable with a single-face lens. The beam expands about 15% from the lens face to the focal plane. Any further reduction in expansion causes light loss, as illustrated by Mb1fL300Ld10N40




Mb1fL300Ld10N40

Lens Ray Trace

The goal of this lens was to produce a multi-beam focal plane with 100% or less delta beam width, i.e. to fully contain the composite beam at the focal plane. That the beam expands beyond this is not a problem because something would be done at the focal plane. However, this is not a good lens. Note how the 40° incident beam does not cover the entire lens width. Optopus eliminated rays that failed, presumably due to reflection but, in any case, due to mathmatical incomputability.

Any modification of this lens to avoid incident light loss increases delta beam width, showing that, even with refractive index 4.0, it is not possible to make a single-face lens with 100% beam containment without unacceptible incident light loss.



GENERAL MULTI-BEAM

These show left and right opening parabola-like focus loci, focus-coplanarity tradeoff, and beam containment.

Mb2fL340Ld09

Lens Ray Trace

This is the only example of a right-open parabola-like locus. It leans only slightly to the right. Any further rightward leaning causes light loss at the lens face.



Mb1fL400Ld53

Lens Ray Trace

This has the most left-leaning parabola-like focus loci. The 40° and 30° foci are already starting to get fuzzy and all of the foci deteriorate rapidly at any further leftward leaning.


Mb2fL440Dw437

Lens Ray Trace

Symmetrical two-face lens focusing 0°, 10°, 20°, 30°, and 40° beams. The 0° (paraxial) focus is very sharp but the focus quality deteriorates with increasing angle. Non-coplanarity is severe. The focal length deviation [(max- min)/average] is 27%. The locus of the foci looks like it might be a wide-bottomed parabola opening toward the light source (to the left).



Mb2fL380Ld55

Lens Ray Trace

This lens flattens the egress to achieve the best possible focus quality but at twice the coplanarity deviation of Mb2fL440Dw437. Any changes from this configuration that increase or decrease coplanarity error reduce focus quality.



Mb2fL200Dw167

Lens Ray Trace

Mb2fL260Ld27

Lens Ray Trace

Mb2fL270Dw250

Lens Ray Trace

Mb1fL340Ld29N20

Lens Ray Trace

Lens Ray Trace