Design Tools - Overview

Prerequisites
DigiLens^TM technology is a switchable holographic optical technology that can be used to great advantage in a wide variety of possible applications. Accurate design of DigiLens^TM based optical systems requires several ingredients:

• An experienced optical designer with a basic knowledge of volume holography;
• A suitable optical design program which is capable of incorporating holograms;
• A specification for the optical system to be designed;
• An appropriately chosen starting optical design configuration which can be optimized using the optical design program to yield a solution which meets the desired performance specifications.

First Order modeling - SpotOnPro
Essentially a DigiLens behaves as a classical volume (Bragg) hologram with the added feature that it is polarization sensitive, providing high efficiency for P-polarized light. It should also be noted that the HPDLC material system that lies at the heart of a DigiLens provides a range of index modulation that is not normally encountered in other Bragg holographic media.

For simple applications, such as laser beam deflectors, the first order geometrical optical properties of a DigiLens can be modeled by treating it as a conventional grating device. The bulk properties of the hologram (ie thickness, index modulation, fringe slant, and absorption) can be ignored, the directions of the diffracted rays being determined solely by :

1. the incident ray orientation,
2. the ray wavelength, and
3. surface fringe grating vector of the hologram or grating.

In general, simple diffraction gratings are not very wavelength and angle selective - their diffraction efficiency is not very dependent on incident angle and wavelength. Incident rays are diffracted into a multitude of transmitted and reflected diffraction orders. However, a volume (Bragg) hologram is angle and wavelength selective (i.e., its diffraction efficiency is high only over a limited incident angle and wavelength range). The selectivity and the magnitude of the diffraction efficiency is dependent on all parameters including those describing the interior of the hologram. This angle and wavelength selectivity is a unique feature which enables a wide variety of applications not possible with conventional optics.

SBG Labs has developed SpotOnPro, an effective and easy-to-use design tool for modelling the basic properties of a DigiLens. SpotOnPro characterizes the diffraction efficiency (DE) and angular diffraction characteristics of a DigiLens using the following input parameters.

• Substrate Geometry
• Design Object point (X,Y,Z) /beam angle
• Design Reference point (X,Y,Z) /beam angle
• Design wavelength
• Construction wavelength
• Grating thickness
• Ambient refractive index
• Grating median refractive index
• Index modulation
• Shrinkage
• Index after curing

Note that SpotOnPro takes into account shrinkage when computing the construction angles required to achieve the design beam angles.

More advanced design tools

While SpotOnPro can provide valuable insight into the performance of a DigiLens® and in certain cases may be more than adequate for component design more sophisticated tools are needed when it comes to imaging and illumination applications.

The three major commercially available optical design programs which handle holograms are:

• ZEMAX® (a product of ZEMAX Development Corporation)
• CODE V (Optical Research Associations)
• OSLO (Sinclair Optics)

Since optical design software is improving all the time, it is difficult to provide a precise comparison of the above programs. The sophistication of the soware tools required to design and model a DigiLens will depend on the nature of the application. Having considered the requirements of a particular optical design, the designer is strongly advised to contact the developers of the above software packages for up-to-date information on the range of hologram design capabilities offered. Some remarks on the general features provided by the above programs follow.

At the very basic level most advance optical design programs provide the ability to model an optical fabricated hologram assuming perfect constructions optics (i.e. with no aberrations imposed on the construction beams). The input data comprises:

• Substrate geometry
• Construction object point (X,Y,Z)
• Construction reference point (X,Y,Z)
• Construction wavelength

More general optically fabricated holograms surfaces in which the construction optics may be completely arbitrary, consisting of multiple lenses, mirrors or even other holograms are also available (eg the ZEMAX® Optically Fabricated Hologram). Aberrations can be introduced into the construction beams to compensate for aberrations in the final design. Any variables set in the construction system automatically become variable in the playback system allowing simultaneous closed loop optimization of the construction and playback systems.

Most advanced optical design programs provide a User Defined Surface (USD) by means of which arbitrary user defined functions can be used to describe surfaces of any form. A user defined surface may have any diffractive properties and may impart any arbitrary phase into a beam. The USD could incorporate a formula or table. Normally the USD would be defined in a separate C or C++ program using the Windows Dynamic Link Library (DLL).

Another feature of more advanced optical design programs is the capability access to basic ray trace data relating to ray energy, position, angle, E vectors and other parameters. Such information may be used to implement custom modeling schemes using a theoretical model or a simple look-up table.

CODEV computes diffraction efficiencies using Kogelnik theory (using an approximation for unpolarized light). Diffraction efficiency may be used as a performance parameter which can be included in the merit function for optimization of the optical design. This ensures that the software will not arrive at a design which has poor diffraction efficiency. Where diffraction efficiency is calculated the normal procedure is to use the Kogelnik approximation for unpolarized light and assume a dielectric hologram with no absorption. This theory assumes that the energy goes into only two waves, the diffracted wave and the zero order (undeviated wave).

Where the properties of the hologram are to be modeled in more detail particularly with regard to characterizing the diffraction efficiency and the effect of shrinkage, CODEV also allows the following parameters to be modeled.

• grating thickness
• grating median index
• index modulation
• volume swelling (fractional) after curing
• index change after curing

It should be noted that other commonly available standard surface types that are not strictly intended to represent holograms, such as Fresnel, Binary and Grating surfaces, may in some applications be used to model particular aspects of a DigiLens.

Normally it will be necessary to design the construction optics in conjunction with the playback optical system. It should be noted that a DigiLens will normally be recorded using UV light. As is the case in conventional holographic recording processes the construction beams geometry will require adjustment for shrinkage. It is common to design a system including HOEs followed by the design of the construction system for each HOE particularly if added phase terms are used. Great care must be exercised to ensure that the beam directions and signs of added phase terms are corrected when transferring the HOE model between the end use and construction optical systems. It is often the case that the local coordinate systems into the two setups are orientated differently.

In addition to software for design of optical imaging systems, there are software packages specifically intended for the design of illumination systems and all three quoted here above do a fine job for conventional optical design. For example, a software package which is able to incorporate holograms is ASAP (Breault Research Organization, Inc., www.breault.com.) ASAP allows the designer to can also specify the relative energy going into each of the diffracted orders. CodeV and Zemax also do the same equally well, but all three have limitations. Please contact SBG for advice and recommendations.

Special design considerations for DigiLens
Most DigiLens applications will require an accurate prediction of light throughput. Such calculations must take into account the 3D dependence of the DigiLens on the (cone) angle of incidence light (which would apply to any Bragg hologram) and (uniquely to a DigiLens) its sensitivity to P-polarized light.

In a commonly used design configuration, in which a ray from an unpolarized source is incident at finite angle of incidence (AOI), in the ZY-plane and emerges normal to the surface of DigiLens the DigiLens has a (separate and distinct) variation in diffraction efficiency vs. angle characteristic in both the YZ-plane and the XZ-plane. It is necessary to properly simulate DE vs AOI in the XZ & YZ planes separately.

One solution is assign a user-defined DE characteristic to the grating via a look-up table, essentially defining the DE as a function of AOI, wavelength and polarization separately for YZ and XZ planes. A convenient method of presenting such information is to use a data file provided for inputting coating data, such as for example the Tabulated Ideal Coating file provided in ZEMAX®. However, such coating files are only suitable when the application does not require independent DE vs. angles characteristics to be specified in the YZ and XZ planes. Where there is a significant between YZ and XZ propagation it will be necessary to employ user-defined surfaces using specially written code that accesses the required DE vs. angle, wavelength and polarization parameters via a formula or look-up table.

Useful references on holographic optical element design
For those who wish to learn more about holography, a variety of holography books and papers are listed below:

• R.R.A. Syms, "Practical Volume Holography," Oxford Science Publications, Oxford (1990).
• L. Solymar, and D.J. Cooke, "Volume Holography and Volume Gratings," Academic Press, London (1981).
• R.J. Collier, C.B. Burckhardt, and L.H. Lin, "Optical Holography," Academic Press (1971).
• H. Kogelnik, "The Bell System Technical Journal," Vol. 48, No. 9, 2909 (1969).
• M.J. Hayford, SPIE Proceedings - Geometrical Optics, Vol. 531, p. 241, (1985).
• M.J. Hayford, SPIE Proceedings - 1985 International Lens Design Conference, Vol. 554, p. 502, (1985).