Heads-up and heads-down displays employing holographic stereograms

A method for preparing and using a holographic stereogram having a perceived image contained therein viewable along a user's line of sight when said holographic stereogram is orientated on a plane nonorthogonal to said line of sight, the method comprising the steps of:

• (a) preparing a set of two-dimensional perspective views of an object;
• (b) transforming said set of two-dimensional perspective views to form a set of transformed views said transformation performed such that
• (i) a user's eyes define vertical and horizontal axes;
• (ii) the tilt of the holographic stereogram is defined by angles .alpha. and .gamma., where .alpha. is measured from the user's line of sight in the plane containing the line of sight and the vertical axis, .gamma. is measured from the user's line of sight in the plane containing the line of sight and the horizontal axis, and .alpha. and .gamma. both equal to 90.degree. corresponds to an untilted stereogram;
• (iii) the line of sight intersects the center of the holographic stereogram;
• (iv) the image is to be perceived by the user to be:
• at a distance Z' from the center of the holographic stereogram along the line of sight, where a positive Z' corresponds to a translation of the image towards the user,
• at a distance Y' from the center of the holographic stereogram in a direction parallel to the vertical axis, where a positive Y' corresponds to a translation of the image upward as seen by the user, and
• at a distance X' from the center of the holographic stereogram in a direction parallel to the horizontal axis, where a positive X' corresponds to a translation of the image to the fight as seen by the user;
• (v) the set of perspective views is defined by a set of .beta. angles, where .beta. equal to zero corresponds to the straight ahead view of the object, positive .beta.'s correspond to movements to the left relative to the object, and negative .beta.'s correspond to movements to the fight relative to the object;
• (vi) each two-dimensional perspective view comprises a set of intensity values in (x',y') coordinates;
• (vii) each transformed view comprises a set of intensity values in (x",y") coordinates;
• and
• (viii) the intensity values in (x',y') coordinates are transformed into intensity values in (x",y") coordinates in step (b) in accordance with the following equations:
• x"=((x'+X').multidot.cos (.beta.).multidot.sin (.alpha.)+Z'.multidot.sin (.alpha.).multidot.sin (.alpha.)-(y'+Y').multidot.cos (.alpha.).multidot.cos (.gamma.-.beta.)/sin (.alpha.).multidot.sin (.gamma.-.beta.))
• y"=y'+Y'
• where at least one of .alpha. and .beta. is different from 90.degree. and at least one of Z', Y', and X' is different from zero;
• and
• (c) preparing the holographic stereogram from the set of transformed views such that the perceived image is substantially orthogonal to the line of sight and is translated relative to the center of the holographic stereogram in a direction of the line of sight.

A method for preparing a holographic stereogram for viewing by a user, the user's eyes defining (i) a line of sight which intersects the center of the holographic stereogram, (ii) a vertical axis, and (iii) a horizontal axis, comprising the steps of:

• (a) preparing a set of two-dimensional perspective views of an object, each of said two-dimensional perspective views comprising a set of intensity values in (x',y') coordinates;
• (b) preparing a set of transformed views comprising a set of intensity values in (x",y") coordinates in accordance with the following equations:
• x"=((x'+X').multidot.cos (.beta.).multidot.sin (.alpha.)+Z'.multidot.sin (.beta.).multidot.sin (.alpha.)-(y'+Y').multidot.cos (.alpha.).multidot.cos (.gamma.-.beta.))/(sin (.alpha.).multidot.sin (.gamma.-.beta.))
• y"=y'+Y'
• where:
• (i) .alpha. is measured from the user's line of sight in the plane containing the line of sight and the vertical axis,
• (ii) .gamma. is measured from the user's line of sight in the plane containing the line of sight and the horizontal axis,
• (iii) .alpha. and .gamma. both equal to 90.degree. correspond to the holographic stereogram being orthogonal to the line of sight,
• (iv) Z' is measured from the center of the holographic stereogram along the line of sight with a positive Z' being towards the user,
• (v) Y' is measured from the center of the holographic stereogram in a direction parallel to the vertical axis with a positive Y' being upward as seen by the user, and
• (vi) X' is measured from the center of the holographic stereogram in a direction parallel to the horizontal axis with a positive X' being to the right as seen by the user, and
• (vii) at least one of Z', Y', and X' is different from zero;
• and
• (c) preparing the holographic stereogram from the set of transformed views.

A method of preparing and using a holographic stereogram having an image contained therein which is tilted with respect to the holographic stereogram such that an intersection of a line of sight with a plane of the holographic stereogram is non-orthogonal but where an intersection of a line of sight with the image is orthogonal with the line of sight, said method comprising the steps of:

• preparing a series of two-dimensional images of an object to be displayed from multiple horizontal perspectives;
• transforming the two-dimensional images to create transformed images which are transformed along a vertical axis;
• distorting the two-dimensional images horizontally to compensate for keystone distortion in the first hologram;
• producing a first hologram using the transformed images by sequentially projecting each of the transformed images through imaging optics onto a vertical segment of a holographic recording plate;
• and
• making a second hologram from a projected image of the first hologram, where the image reconstructed when said second hologram is exposed to appropriate reconstructive illumination appears to occupy a plane angled with respect to the plane occupied by the second hologram.

A method of preparing and using a holographic stereogram from a preexisting set of two-dimensional images where the holographic stereogram has an image contained therein which is tilted with respect the holographic stereogram such that the intersection of a line of sight with a plane of the holographic stereogram is non-orthogonal but where the image of the hologram appears to be orthogonal with the line of sight, said method comprising the steps of:

• digitizing the preexisting set of two-dimensional images to create digitized images;
• transforming the two-dimensional images by relocating the intensity values of the digitized images on a pixel-by-pixel basis to create transformed images having vertical transformation;
• producing a first hologram using the transformed images by sequentially projecting the transformed images onto a diffusion screen, and moving a movable a slit aperture in front of a holographic recording plate to image the contents of the diffusion screen thereon;
• and
• making a second hologram from a projected image of the first hologram, where the image reconstructed when said second hologram is exposed to appropriate reconstructive illumination appears to occupy a plane angled with respect to the plane occupied by the second hologram.

A method of preparing and using a hologram stereogram having an image contained therein which is tilted with respect to the holographic stereogram such that an intersection of a line of sight with a plane of the holographic stereogram is non-orthogonal but where an intersection of a line of sight with the image is orthogonal with the line of sight, said method comprising the steps of:

• preparing a series of two-dimensional images of an object to be displayed from multiple horizontal perspectives;
• transforming the two-dimensional images to create transformed images by altering the two-dimensional images which are defined in a two-dimensional (x',y') coordinate system to transformed images defined in a two-dimensional (x",y") coordinate system where centers (x',y'=0,0 and x",y"=0,0) of these coordinate systems are coincident;
• producing a first hologram using the transformed images by sequentially projecting each of the transformed images through imaging optics onto a vertical segment of a holographic recording plate;
• and
• making a second hologram from a projected image of the first hologram where, the image reconstructed when said second hologram is exposed to appropriate reconstructive illumination appears to occupy a plane angled with respect to the plane occupied by the second hologram.