ZDC thanks Eddie Judd of Davin Optronics for many useful discussions, and Robin Hull, also of Davin Optronics, for permission to use his test image in this article.

Imagine you were tasked with designing some imaging optics for a customer who was not an optics specialist. You may produce three designs: a singlet, a doublet, and a 5-element eyepiece. Each design has its own price/performance point.

Now, your customer understands price very well: but how do you communicate things like vignetting, field curvature, astigmatism etc to a non-optics specialist? The Geometric Bitmap Image Analysis (GBIA) feature in ZEMAX is extremely helpful in showing customers what images will look like when you "look-through" the built lens. It communicates far more directly than ray-fan plots and the like.

A note on Versions: the GBIA feature has been in ZEMAX for many years. However, the August 2006 and subsequent versions benefit from a greatly improved sampling algorithm that gives results with better signal/noise ratio for fewer rays traced. This article was written with the August 2006 release. Users of earlier versions will be able to get the same results, but will require substantially longer time to do so.

When a sequential optical design is being optimized or toleranced, we normally test system performance by using several analysis features that test the response of the system to an infinitesimal point on the object surface. Such features include ray fans, OPD plots, MTF, PSF and many more. The Geometric Bitmap Image Analysis feature lets you place a high resolution object scene on the object surface, and to trace rays from this scene correctly weighted by wavelength, field, apodization and source brightness. A schematic is shown below.

{Note that this image was produced by the non-sequential mode of ZEMAX: see the last page of this article for full details.}

The object scene is represented by a source bitmap, which can be a .BMP or .JPG file. Rays are traced using the defined object aperture and field towards the pupil of the optical system, and on through to the image plane (or other specified surface). In the detection surface we place a pixellated detector which receives the rays and builds up an image of the source bitmap as seen through the lens. This image includes the effects of all aberrations, vignetting at apertures and optionally of thin-film coatings and glass absorption too.

In additional to all the normal editor data, there are two pieces of information that ZEMAX must be given. The first is information on the size and resolution of the source scene. In the example we will use in this article, the source is a color LCD screen of specified dimensions and 640x480 (VGA) resolution. We will image this scene through three different optical systems, onto a detector which is also VGA resolution. Here is the source scene we will use:

 

and here is the settings dialog for the geometric Bitmap Image Analysis (GBIA) feature:

For full details of how to use the settings, see the User's Guide. Here is a brief description of the most important parts:

• Field Y Size defines the y-height of the source bitmap in whatever units the field is measured in. In our examples the field is object height in mm, and so the full width of the bitmap on the object plane is 13.8 mm. The x-width is then determined from the aspect ratio of the bitmap
• Parity allows us to account for systems that invert. This will re-invert the image so that we see it right-side-up, if we wish to.
• Input defines the source bitmap or .jpg scene that is to be used. This file must be located in the {zemaxroot}/imafiles folder
• Rays/Pixel determines how many rays should be traced from each pixel. This directly affects the signal/noise ratio, at the expense of calculation time. 1 ray/pixel is usually fine for setting the feature up correctly, 10 gives quick results, 100 gives very good images and 1000 or more gives photo-realistic images
• X-Pixels, Y-Pixels, X Pixel Size, Y pixel size allows you to define the size and resolution of the detector
• Show Source Bitmap lets you choose to render the input scene, and was used to produce the top graphic
• Output writes the resulting GBIA results to a .jpg or .BMP file. This is important because what you see via the Analysis window is viewed "through" your monitor's resolution, and so may be significantly downsampled or demonstrate Moiré. It also prevents you from losing data if you accidentally close the window before saving the results!

In the attached zip file (which can be downloaded from the last page of this article) are three lens file: a singlet, doublet and 5-element eyepiece design. These lenses are not intended to be the best possible design: in fact the first two are deliberately poor lenses just to demonstrate this feature!

Here is the source bitmap imaged through the singlet lens:

This image was produced using 10 rays/pixel, and ran in 5 seconds on a Pentium-M 1.6 GHz laptop. Increasing the number of rays to 100/pixel gave the following result in about 40 seconds:

You can see clearly the distortion at the edges of the image and the vignetting which causes the image to darken at the edges. Field curvature and astigmatism cause the focal quality to drop off very quickly as we move away from the center of the image. Moving to the doublet lens, and tracing 100 rays/pixel gives us the following, also in about 40 seconds:

Some of the detail in the center is better resolved, but the design is clearly still dominated by distortion and field curvature. It would be hard to convince a customer that the extra cost of the doublet was justified by the improved performance!

Moving to the five-element eyepiece, which is significantly better optimized, we get:

This is a clearly better result. The distortion is gone (some higher order distortion can still be seen on the higher-resolution images shown later), and the field curvature is gone. The lady in the bottom right hand corner can be clearly seen instead of just being a smudge.

This lens uses 5 elements and requires ray-aiming turned on, and so this took around 5 minutes to trace on the same laptop as the previous scenes. So, moving to my 2-CPU workstation (which has two real Pentium 4 processors plus hyperthreading, so it looks like a 4-CPU machine), I set the GBIA to 1000 rays/pixel and obtained this in about 20 minutes:

Remember that ZEMAX is very well multi-threaded, which means that it can trace one group of rays on one processor, and another group on another. This makes great use of today's multiple-CPU and multiple-core machines. See this article for more details.

This image is virtually indistinguishable from the original image. However, this is a 640x480 pixel image displayed in a much smaller window. Here is the full jpg file saved automatically by the GBIA feature:

Remember that this is a ray-tracing result and is not the original image! If this is printed out on good quality photo-paper it gives a photo-realistic impression of the real system performance. In fact, the differences between it and the original bitmap are due to the detector resolution more than the optics themselves, so this output really does represent what this detector sees.

The designers of digital cameras (cameras with CCD detectors) have a significant advantage over the designers of film-based cameras. Lenses for film-based cameras must produce a high-quality image directly on the film plane, and there is no possibility for post-processing. When the detector is a CCD chip, and the camera has an on-board computer, there is significant scope for electronic post-processing of the image to remove aberrations.

The simplest example is distortion correction. Because distortion only affects the location of the image, and does not affect the quality, it is possible to un-distort the image electronically. This relieves the lens designer of the need to minimize a significant aberration. Much work is also being done on compensating other aberrations, given a knowledge of the OTF of the lens. Using the GBIA feature allows such image correction algorithms to be tested prior to building expensive prototype optics, and the work we have done recently on improving the speed of this feature means that this work can be done in almost real time.

Note that diffraction is not considered by the GBIA: if diffraction effects are important, look at the Diffraction Image Analysis and Extended Diffraction Image Analysis features instead.

Finally, the same calculation can be performed non-sequentially if desired, especially if monochromatic images are required. The non-sequential SLIDE object can be used to place a .bmp or .jpg graphic in an optical system. It can also be used in hybrid-mode, so that you can place a slide object at any location in a sequential optical system too.

The advantages of performing these calculations in non-sequential mode include:

• More realistic modeling of sources is possible in non-sequential mode, including the use of measured source data like Radiant Sources. See this article for more information on source modelling.
• The effects of ghost pupils and images on the final image can be seen
• The effects of opto-mechanical stray light, in which light reflects from the mechanical components of the system can be included

This disadvantage is mainly speed: non-sequential ray-tracing is inherently slower than sequential, and ray-tracing CAD objects is slower than tracing parametric optical objects. The other disadvantage is that the NSC detector must be traced one wavelength at a time, the data exported, and the recombined to produce the full color image (this is not necessary if the image is monochromatic). Therefore the sequential analysis should be performed first. If the sequential system gives inadequate performance, then nothing that is considered by the non-sequential ray-trace will improve things: the effects considered by the non-sequential trace generally only degrade performance.