lenticular photography by Yitzhak Weissman

Lenticular Photography

3D lenticular pictures • Pros: • Can be viewed naturally without any viewing aids. • Can be printed using standard printing methods. • Cons: • The depth display capability is very limited. • Price per unit in small quantities is high: approximately x10 compared to conventional print.

Creation of a 3D lenticular picture â&#x20AC;˘ The process of converting a real object to a 3D lenticular picture requires special tools and software, as well as skill and expertise in several disciplines: photography, image processing, and printing. â&#x20AC;˘ Fortunately, this process can be divided into two tasks: photography and printing. The interface between these tasks is the lenticular sequence: a series of (processed) photographs of the object or the scene.

Photography

Sequence

Printing

Object image

The lenticular sequence • The lenticular sequence is a group of photos of an object (or a scene) taken from a group of points (shooting points). • Any pair of photographs in the sequence must be a stereo pair and therefore contain a zeroparallax plane (aka ‘stereo window plane’). • The zero-parallax planes will be mapped to the picture plane. • Therefore, all photographs must share the same zero-parallax plane (sequence registration).

Zero-parallax plane

The art of lenticular photography

High visual quality & Low depth display

Low visual quality & High depth display

• In 3D lenticular pictures there is a trade-off between visual quality and depth display. • The optimal tradeoff depends on the image content and the artist’s preferences. • Here we will aim at the balanced trade-off, which fits most cases.

Visual quality

Depth display

Designing the photography session • The lenticular sequence • The geometry • The increment • The number of photographs • The photographs pixel sizes

The lenticular sheet • The lenticular sheet is an array of cylindrical lenses. • Two parameters are most important for lenticular photography: the lenticules density and the sheet thickness. • The lenticules density is normally quoted in number of lenticules per inch and denoted by “lpi”. • Popular lpi values are 60, 40, and 20. • Another important characteristic is the viewing angle. It is determined by the lenticules density and the sheet thickness. In sheets designed for 3D pictures the viewing angle is typically between 25 to 35 degrees.

The shooting points geometry • There are two common geometries for lenticular photography: circular and linear. • In the linear shooting geometry, all shooting points lie on a horizontal line and the distances between adjacent points are equal. The camera is displaced parallel to itself. • In the circular geometry, all shooting points lie on an arc, and the angles between any two adjacent points (with respect to the arc center) are equal. The camera always points to the arc center. • Both geometries give identical results (practically). The angular geometry is more convenient for both practice and presentation, and it will be used here.

Visual continuity in lenticular pictures • As the observer moves with respect to the picture, the images displayed by the picture will change. • In a continuous picture, these changes are unnoticeable, and the picture will display a continuous animation. • The horizontal resolution element in a lenticular picture is the lenticule width. Therefore, to achieve continuity, the parallaxes between any two successive images (the incremental parallaxes) in the lenticular sequence must be smaller than the width of the lenticules. • To achieve maximal depth display, the incremental parallax value is set to the lenticule width.

Displayed 3D position • An object point with a non-zero parallax will be displayed at a certain distance from the picture plane. • The displayed distance hmax for incremental parallax which equals the lenticule width is given by

hmax

N ⋅t = n

where N is the number of photographs in the sequence, t is the thickness of the lenticular sheet and n is its optical index of refraction (with typical values between 1.56 to 1.6). Note: unlike in stereo displays, the displayed protrusion is independent of the viewing distance.

Adjusting the zero-parallax plane for maximum depth display

hmax

• The displayed depth is the sum of the maximal displayed protrusion and recession. • If the zero-parallax plane passes through the center of the scene, then the maximal depth Dmax that can be displayed is given by Dmax = 2 ⋅ hmax

Zero parallax plane at center Depth = 2hmax Vision plane

hmax

2N ⋅ t = n

Zero-parallax plane at back

• In all other positions of the zero-parallax plane, the displayed depth will be smaller.

Depth < 2hmax

hmax

The number of resolvable images in a lenticular picture • Since the maximal displayable depth is proportional to N, there is a strong motivation to use as large values of N as possible. • However, a lenticular picture can resolve only a finite number of images Nr. Using values of N which exceed Nr will cause blending of adjacent images in the sequence, resulting in blurring. • The number of resolvable images determines the amount of depth that can be displayed by a lenticular picture. • As such, it is the most important figure of merit for a lenticular picture. Its value is determined by a combination of several mechanisms. In pictures done with inkjet printers, the limiting mechanism is the printer resolution. • Approximate value of Nr for Epson inkjet printers: 360/lpi. • Approximate value of Nr for Canon and HP inkjet printers: 300/lpi.

The blurring effect The blurring increases with the distance from the picture plane and creates a visual effect like the familiar â&#x20AC;&#x153;depth of fieldâ&#x20AC;? in conventional photography.

Original

Blurred

The maximal displayable depth in some popular lenticular sheets (360ppi printer) Values of the maximal displayable depth of continuous pictures for three popular lens sheets used for 3D lenticular pictures, Epson printer.

Lenticules density (lpi)

Sheet thickness (mm)

Maximal depth (mm)

1.3

3.5

Example: 20lpi and 40cm wide picture

Determining the depth scaling factor

8 24 48 Original object

x2 scaled down to fit the picture aperture

x3 depth scaled down for display

Example (contd.) The depth scaling factor determines the photography (angular) increment:

increment =

( depth scaling factor ) ⋅ ( viewing angle ) N

For the 20lpi lens N = 18 and the viewing angle (in this example) is 32°. With a 1/3 depth scaling factor, the angular increment value is 0.6°. If you are shooting from 5m distance, the linear increment will be 5cm. Note: you can increase the displayed depth by increasing N but keeping the same value of the increment (0.6°). This will introduce blurring.

The visual resolution of a lenticular picture • The smallest graphical element width that can be displayed in a lenticular picture is the lenticule width. • In other words, the visual pixel density of a lenticular picture in the horizontal direction is the same as the lenticules density, and the number of displayed pixels in the horizontal direction is the number of lenticules. • There is no limitation on displayed pixel density in the vertical direction.

Required pixel sizes • When horizontal and vertical pixel densities in a picture are different, the perceived pixel density is the smaller one between the two. • Therefore, the minimal requirement on the pixel density in a lenticular sequence (in both directions) is the lenticules density. • The raw photographs undergo many transformations (both in the photography and the printing stages). These transformations reduce their resolution. • Therefore, it is recommended to use a pixel density which is twice the lenticules density in both dimensions.

Required pixel size (contd.): typical values • A lenticular picture has typically about 500 lenticules regardless of size. • Lenticular photograph width rule of thumb: 1000 pixels (regardless of size). • Lenticular photograph height rule of thumb: 1000 pixels divided by the aspect (regardless of size). • In high quality conventional print of 300ppi density, 1000 pixels span only 85mm.

Lenticular sequence preparation In most cases raw photographs need registration. Other common processing operations include zero-parallax plane adjustment and insertion of intermediate frames.

Raw photographs

Processing

Lenticular sequence

Registration of a sequence of images • There are several software packages which perform a fully or partially automatic image registration. • These software packages do decent job in most cases, but in some cases, they yield unsatisfactory precision or even fail. • Fcarta, a free software from Pop3DArt, can be used to perform manual registration with utmost accuracy in all cases. It relies on mounting physical control points in the scene. Scene with physical control points for registration with Fcarta

Examples of image registration

SPM (semi-automatic)

Fcarta (manual)

Cosima (automatic)

Conversion of stereo pair to lenticular sequence • Attempts to convert a stereo pair to a lenticular sequence by automatic interim frames generation usually fail. • Recently Facebook introduced 3D photo display technology for mobile phones which became very popular. It is based on the use of depth-maps. • Depth-maps can be created from stereo pairs using existing software packages • A stereo pair with a depth-map can be converted to a lenticular sequence. This method has decent chances of success.

Examples of stereo pairs converted to lenticular sequences via depth-maps

Summary • You can use existing lenticular print-on-demand services to print a 3D lenticular picture. • The photographs are submitted as a lenticular sequence. • You have learned how many photographs are needed and what is the photography increment to achieve a high visual quality image with optimal depth display. • The required number of pixels in the horizontal direction is approximately 1000. • Techniques: registration, conversion of stereo-pairs.

Links • 3D photography tutorials: • https://www.midwestlenticular.com/photographing-for-3d-lenticular-printing • https://youtu.be/RwfGKhqSaZ0 • Image registration • https://www.pop3dart.com/fcarta-software (free) • http://stereo.jpn.org/eng/stphmkr/ (free) • http://www.cosima-3d.de/cosima_serie.html (limited free version)

Links (contd.) • Zero-parallax plane adjustment (free) • http://www.3dmix.com/eng/download.php • Insertion of intermediate frames • After Effects (Adobe) • Creation of a lenticular sequence using a depth-map: • http://stereo.jpn.org/eng/stphmkr/ (free) • http://3dstereophoto.blogspot.com/p/software.html (free)