Dappled Photography: Mask Enhanced Cameras for
Heterodyned Light Fields and Coded Aperture Refocusing

Ashok Veeraraghavan, Ramesh Raskar, Amit Agrawal, Ankit Mohan and Jack Tumblin

Low res pdf
High res pdf

SIGGRAPH Talk Slides

Matlab Code

Coded Aperture Photography (a part of this paper)

Errata: Equations 11 and 12 have error in published version which has been corrected in online pdfs.
Detailed derivation of equations 10,11 and 12 (not in paper)

Frequently Asked Questions

Captured Photo,
                Recovered Full res photo, Digitally refocussed results


We describe reversible modulation of 4D light field by inserting a patterned planarmask in the optical path of a lens based camera. We can reconstruct the 4D light field from a 2D camera image without any additional lenses as required by previous light field cameras. The patterned mask attenuates light rays inside the camera instead of bending them, and the attenuation recoverably encodes the ray on the 2D sensor. Our mask-equipped camera focuses just as a traditional camera might to capture conventional 2D photos at full sensor resolution, but the raw pixel values also hold a modulated 4D light field. The light field can be recovered by rearranging the tiles of the 2D Fourier transform of sensor values into 4D planes, and computing the inverse Fourier transform.

We also show how a broad-band mask placed at the lens enables us to compute refocusing at full sensor resolution for images of layered Lambertian scenes. This partial encoding of 4D ray-space data enables editing of image contents by depth to remove or suppress unwanted occluders, yet does not require computational recovery of the complete 4D light field.

Figure 1. Prototype camera designs derived from our Fourier domain theory of mask-enhanced cameras.

Graphical Illustration of Computing 4D Light Field from 2D Photo

Consider a scene consisting of several cones at different depths. If we take an image with a traditional camera, we get the photo shown above. The magnitude
of the 2D FFT of the image shows high energy at low frequencies. This is a well known fact that most energy in natural images is concentrated
in low frequencies.

Now consider taking a 2D photo of the same scene with our Heterodyne Light Field Camera. In this new camera, we place a cosine mask near the
sensor. We get an image shown as below.

Although this image looks similar to the previous photo captured using a traditional camera, notice the effect of mask on the input photo. The mask
casts a soft shadow on the sensor. It dapples the light reaching the sensor. In theory, mask modulates the incoming 4D light field to make spectral

Now consider the 2D FFT of this new image. Notice that the spectral replicas are clearly seen!!!. Compare this FFT image with the previous FFT image to
visualize the differences.
These replicas are due to the cosine mask placed near the sensor. The cosine mask modulates the incoming 4D light field.
In this example, the mask has 4 harmonics, or 4*2+1 = 9 impulses in its frequency response. Thus, we get 9*9=81 replicas in both x and y direction.

Now lets see how we can obtain the 4D light field from the modulated 2D photo captured from our Heterodyne Light Field Camera. The entire algorithm
is shown graphically below.


1. Compute the 2D FFT of the captured 2D photo.
2. We know that we will get 9*9 replicas due to the physical mask placed near the sensor. Rearrange these 81 tiles into 4D.
3. Compute the inverse 4D FFT to get the light field.

Click on the above image to see a video (ViewCones1.avi) of different 'views' obtained from the light field. These views are essentially images that we
would obtain if we look through a narrow aperture on the lens at different positions.

Related Papers:

Coded Exposure Photography: Motion Deblurring using Fluttered Shutter, SIGGRAPH 2006
Resolving Objects at Higher Resolution from a Single Motion-Blurred Image, CVPR 2007