Metameric Varifocal Holograms

David R. Wal­ton, Koray Kavak­lı, Rafael Kuffn­er dos Anjos, David Swapp, Tim Weyrich, Hakan Urey, Antho­ny Steed, Tobias Ritschel, and Kaan Akşit

Paper | Video | Sup­ple­men­tary Mate­r­i­al | Code (Holo­gram Opti­mi­sa­tion) | Library (Metamer­ic Loss)


Com­put­er-Gen­er­at­ed Holog­ra­phy (CGH) offers the poten­tial for gen­uine, high-qual­i­ty three-dimen­sion­al visu­als. How­ev­er, ful­fill­ing this poten­tial remains a prac­ti­cal chal­lenge due to com­pu­ta­tion­al com­plex­i­ty and visu­al qual­i­ty issues. 

We pro­pose a new CGH method that exploits gaze-con­tin­gency and per­cep­tu­al graph­ics to accel­er­ate the devel­op­ment of prac­ti­cal holo­graph­ic dis­play sys­tems. First­ly, our method infers the user’s focal depth and gen­er­ates images only at their focus plane with­out using any mov­ing parts. Sec­ond, the images dis­played are metamers; in the user’s periph­er­al vision, they need only be sta­tis­ti­cal­ly cor­rect and blend with the fovea seam­less­ly. Unlike pre­vi­ous meth­ods, our method pri­ori­tis­es and improves foveal visu­al qual­i­ty with­out caus­ing per­cep­tu­al­ly vis­i­ble dis­tor­tions at the periphery. 

To enable our method, we intro­duce a nov­el metamer­ic loss func­tion that robust­ly com­pares the sta­tis­tics of two giv­en images for a known gaze loca­tion. In par­al­lel, we imple­ment a mod­el rep­re­sent­ing the rela­tion between holo­grams and their image recon­struc­tions. We cou­ple our dif­fer­en­tiable loss func­tion and mod­el to metamer­ic var­i­fo­cal holo­grams using a sto­chas­tic gra­di­ent descent solver. We eval­u­ate our method with an actu­al proof-of-con­cept holo­graph­ic dis­play, and we show that our CGH method leads to prac­ti­cal and per­cep­tu­al­ly three-dimen­sion­al image reconstructions.


We pro­vide source code for the metamer­ic loss and holo­gram opti­mi­sa­tion sep­a­rate­ly, so that the metamer­ic loss can be used on its own for oth­er pur­pos­es if desired.

The metamer­ic loss is part of the odak com­pu­ta­tion­al optics library. To use this we rec­om­mend installing odak using pip , for example:

$ pip install odak

Depend­ing on your envi­ron­ment you may need to call pip3 rather than pip . Please ensure you have installed ver­sion 0.1.9 or new­er. For details on instal­la­tion and how to use the loss func­tion, please see the odak doc­u­men­ta­tion.

The holo­gram opti­mi­sa­tion code is locat­ed here. Please see the repos­i­to­ry README for instal­la­tion and usage instructions.


  title={Metameric Varifocal Holograms},
  author={Walton, David R and Kavakl{\i}, Koray and Dos Anjos, Rafael Kuffner and Swapp, David and Weyrich, Tim and Urey, Hakan and Steed, Anthony and Ritschel, Tobias and Ak{\c{s}}it, Kaan},
  booktitle={2022 IEEE Conference on Virtual Reality and 3D User Interfaces (VR)},


This work was fund­ed by the EPSRC/UKRI project EP/T01346X/1.