Longitudinal Magnification Research Articles

Dual Fresnel mirror system for 360 degree viewable three-dimensional displays

360-degree viewable three-dimensional (3D) display systems have gained considerable attention for the unique manner in which they display objects. Most of the optical display devices in these systems employ two parabolic mirrors facing each other separated by a distance equal to the focal length of the mirrors. However, the current configuration is limited to unity magnification and provides a small image relative to the volume of the system. This paper presents a novel 3D display system based on two Fresnel mirrors with different focal lengths facing each other. The distance between the mirrors can be adjusted to alter the magnification of the resulting 3D image. Wave-optics analysis of an optical dual-lens system equivalent to the proposed dual-mirror system was used to simulate the image distance, the transverse and longitudinal magnification, and the minimum length of the proposed system. This paper also addresses issues pertaining to the design and manufacture of Fresnel mirrors. An experiment system using Fresnel mirrors with focal lengths of 60mm and 90mm clearly demonstrated the efficacy of the proposed scheme in terms of 3D image magnification.

Holographic waveguide head-up display with 2-D pupil expansion and longitudinal image magnification.

Head-up displays (HUDs) are used in aircraft to overlay relevant flight information on the vehicle's externals for pilots to view with continued focus on the far field. In these systems, the field of view (FOV) is traditionally limited by the size of the projection optics. Though classical HUD systems take a significant amount of space in the flight deck, they have become a necessity in avionic transportation. Our research aims to reduce the size of the HUD footprint while offering a wide FOV projected in the far field with an expanded pupil. This has been accomplished by coupling the image-bearing light into a waveguide under total internal reflection conditions, redirecting that light in the orthogonal direction, and then outcoupling the light toward the pilot. Each step was achieved using holographic optical elements. The injection hologram has optical power to obtain longitudinal magnification, whereas the redirection hologram expands the pupil in one dimension and the extraction hologram expands the pupil in a second dimension. Varying diffraction efficiency along the direction of the light propagation ensures even image intensity throughout the expanded pupil. We used ray tracing optical simulations to optimize the design of the system and present a fully operational demonstrator of the HUD. This HUD produces an image with a FOV of 24°×12.6° at a viewing distance of 4.5 in. (114 mm) from the waveguide, with infinite longitudinal magnification and 1.9× by 1.6× horizontal and vertical pupil expansion, respectively.

Modified correlation method to autofocus particles in digital in-line holography

A method is proposed to automatically evaluate the focal planes of spherical particles. This method compares the correlation coefficients of multiple reconstructed planes relative to a reference plane. The particles are located where a minimum correlation is found, and reconstructions are made using an angular spectrum propagator. The Hough transform is employed to segment the hologram, thereby enabling the detection of circular shapes, such as Airy patterns, and the edges of the particles themselves. The autofocus is improved by creating a correlation matrix using an iterative process, which reduces the computational cost of the particle display processes in their respective focal planes. A theoretical model was studied to estimate the longitudinal and transverse magnifications of the focused particles caused by the influence of aberrations in the reconstruction of digital holograms due to the spherical reference wave used. Experimentally, laser light was used to illuminate 5-μm latex particles, which was recorded by a CCD camera with a 9.9-μm pixel size. The reconstructions measured an average particle radius of 71.3±16.3 μm in the average focal plane, which was estimated to be 60.65±0.22 mm from the hologram where the magnifications were considered.

Annular solid-immersion lenslet array super-resolution optical microscopy

We describe a novel solid-immersion lenslet array, micro-fabricated in a chip form in the high-index (3.45) gallium phosphide. The innovatively designed lenslet features an annular aperture with appropriately patterned light absorbers and antireflection coatings. The array chip is easy to handle and enables the direct deposition of the specimen of interest onto its back-plane for tight adhesion and good optical coupling. The ensuing diffraction from the near field can yield supercritical rays inside the high-index lenslet and can, therefore, overcome the refraction and critical-angle limitations. This model showed agreement with the experimental observation of the solid-immersion fluorescence microscopy imaging, in which the refracted rays were completely blocked by the annular aperture. A large longitudinal (depth) magnification effect was also predicted and showed agreement with experiment. The annular lenslet's additional advantages of improved resolution and contrast were also discussed. Resolution of nested-L patterns with grating pitch as small as 100 nm was experimentally demonstrated. The demonstrated annular solid-immersion lenslet array concept is promising for a wider use in super-resolution optical microscopy.

Dielectric interface effects in subsurface microscopy of integrated circuits

We investigate the defocus and image quality affected by a dielectric interface on high numerical aperture focusing of linearly polarized illumination in aplanatic mode. Theoretical and experimental demonstration is performed on subsurface backside microscopy of silicon integrated circuits, showing that the high longitudinal magnification provided by solid immersion lens microscopy allows the observation of significant astigmatism. It is shown that a 50micron longitudinal displacement of the objective lens with respect to the sample is necessary to achieve maximum resolutions in two directions.

Integral floating‐image display using two lenses with reduced distortion and enhanced depth

Abstract— An integral floating display (IFD) with a long depth range without floating lens distortion is proposed. Two lenses were used to reduce barrel distortion of the floating lens and three‐dimensional (3‐D) image deformation from object‐dependent longitudinal and lateral magnifications in the floating‐display system, combined with an integral imaging display. The distance between the floating lenses is the sum of their focal lengths. In the proposed configuration, lateral and longitudinal magnifications are constant regardless of the distance of the integrated 3‐D images, so the distortions from the distant‐dependent magnifications of the floating lens do not occur with the proposed method. In addition, the proposed floating system expands the depth range of the integral imaging display. As a result, the display can show a correct 3‐D floating image with a large depth range. Experimental results demonstrate that the proposed method successfully displays a 3‐D image without floating lens distortions across a large depth range.

Experimental demonstration of longitudinal magnification

We describe an experiment which enables the observation of longitudinal magnification forthe real image of a three-dimensional (3D) object formed by a converging lens. Theexperiment also shows the absence of longitudinal inversion. Possible reasons formisconceptions with respect to real images and longitudinal inversions are discussed and ateaching sequence to suppress them is suggested. As an illustration, an experiment clearlyshowing the presence of longitudinal inversion for the real image of a 3D object formed by aconcave mirror is also described.

3D object scaling in integral imaging display by varying the spatial ray sampling rate

In this paper, we present a method to scale (that is, to enlarge or reduce) three-dimensional integral images of objects. The scaling is achieved by controlling the spatial ray sampling rate of elemental images in the pickup procedure of the object. The sampling is obtained by using a moving array-lenslet technique (MALT) during the recording stage. In the display process, a stationary display lenslet array is used. The lateral and longitudinal magnifications obtained with the proposed method are the same, therefore three-dimensional image distortion can be avoided. To illustrate the feasibility of our method, experiments are performed to magnify a small object in three-dimensional space.

Correction: “Longitudinal Magnification Drawing Mistake” [Phys. Teach. 42 (1), 31–33 (Jan. 2004)

Correction: “Longitudinal Magnification Drawing Mistake” [<i>Phys. Teach.</i> 42 (1), 31–33 (Jan. 2004)

Longitudinal Magnification Drawing Mistake

Lateral magnification in image formation by positive lenses, mirrors, and dioptrics is usually appropriately developed in most optics textbooks.1–9 However, the image of a three-dimensional object occupies a three-dimensional region of space. The optical system affects both the transverse and the longitudinal dimensions of the object and, in general, does it in different ways. The magnification in the direction of the optical axis (the longitudinal magnification) is seldom treated. In several texts, the concept of longitudinal magnification is not even considered. Symmetrical objects (such as arrows) are used and their images appear laterally inverted. It is not shown how a longitudinally nonsymmetric object is imaged. One of the few books where this subject is well treated is in the textbook by Hecht.10 We have repeatedly verified in our classes that there is some confusion related to this subject. Students tend to believe that the image is longitudinally symmetric with respect to the lens optic center. Some prestigious texts commit the same mistake. In addition, a very nice optics book,11 a catalogue of optical hardware,12 a worldwide scientific magazine,13 a paper in an optics journal,14 and a Spanish encyclopedia,15 for example, have also been found to contain this error in drawing the image of a three-dimensional object formed by a positive lens. In this paper we suggest that the teaching of longitudinal magnification should be done with some care and we include a figure showing a properly drawn image.

Focused-image holography as a dense-spray diagnostic

The denser regions of sprays need to be probed for us to understand further the basic phenomena of the breakup of a bulk liquid into droplets and the subsequent drop dynamics. The instruments currently available to spray diagnosticians, the Malvern spray analyzer and the phase/Doppler particle analyzer, cannot be used in the denser regions of the spray and in regions where ligaments or nonspherical droplets exist. Holography, as applied in the past, has permitted the interrogation of nonspherical drops but in general has been applied to droplet-dominated dilute regions of sprays. Using a focused-image holographic system, with the advantages of an imaging lens and side lighting, we can probe highly complex regions of sprays, such as those that include bubble explosions and complex ligament formation at the nozzle exit. In this paper we present components of a focused-image holographic system for spray analysis, advantages and limitations of that system, and how the longitudinal magnification varies as a funct on of the length of the object along the optical path.

The X-Ray Magnification of the Hip for Preoperative Planning: A New Technique

Precise pre-op planning is fundamental for surgical precision in fit and fill of uncemented prostheses, and reliable and comparable radiographs are necessary for the early diagnosis of loosening. All this can be obtained with a given X-ray magnification factor. The Authors prove that the routinely used methods are misleading and suggest a new technique to obtain a uniform and/or measurable magnification in the A.P. radiograms of the hip. The method gives accurate measurements within a few tenths of a millimetre. It is based on the knowledge of the femoral position in relation to the X-ray film, obtained with a lateral radiographic view, and on mathematical calculation to obtain the X-ray focus height and position. Also in the case of a flexed and externally rotated hip, the non-uniform longitudinal and transverse magnifications can be measured.

Propagation of focal shift through axisymmetrical optical systems

Focusing of an un-apertured spherical gaussian beam is re-examined on the basis of transformation of the focal shift, namely, transformation of the deviation of focal spot from its geometrical optics position to the plane containing the waist of gaussian beam. It is found that the relative focal shifts for gaussian beams in the object and image spaces of an axisymmetric optical system are coupled by the same geometrical optics relationship concerned with longitudinal magnification of small objects on the axis. However, the relative focal shifts in the object and image spaces are not necessarily small quantities, when the law of small object magnification is applied to describe the transformation of focal shift.

Magnification effect and color blur behavior in holography

This paper describes the spatial behavior of the hologram image as a function of the geometric setup used in the recording and reconstruction steps. Given the equation of the holographic image and using paraxial theory and the synthetic division method, values of the longitudinal and lateral magnification are obtained. The location and magnification of the holographic image are found when the distance between the holographic plate and the object is changed. For white light reconstruction and 3-D scenes the effect of color blur can be expressed in terms of the parameters associated with the optical system that forms the image on the hologram and the recording geometry.

Design Considerations For Multiple Telescope Imaging Arrays

The basic principles for designing and implementing multiple telescope imaging arrays are presented. A generalized treatment is formulated that permits determination of the amount of residual errors that can be tolerated in lateral and longitudinal pupil geometry matching, magnification matching, azimuthal asymmetry, and telescope boresighting. A specific design goal is a modular system of independent telescopes configured to have the equivalent performance of a monolithic aperture of the same diameter as the array. This telescope array, known as the Multipurpose Multiple Telescope Testbed (MMTT), is designed to provide high resolution imagery over a wide field of view. The requirement for wide field of view performance imposes rigid tolerances that must be satisfied at every stage of development. The work described here derives the subsystem tolerances that must be met. Special means by which some of the more rigid requirements can be satisfied are also briefly described.

Application of longitudinal magnification effect to magnification stereoscopic angiography: a new method of cerebral angiography.

A new method of stereoscopic cerebral angiography has been developed which employs 2X radiographic magnification. In order to obtain the same depth perception in the object as with conventional contact stereoscopic angiography, one can made the x-ray exposures at two focal spot positions which are separated by only 1 inch (2.5 cm), whereas the contact technique requires a separation of 4 inches (10 cm). The smaller distance is possible because, with 2X magnification, the transverse detail in the object is magnified by a factor of two, but the longitudinal detail, which is related to the stereo effect, is magnified by a factor of four, due to the longitudinal magnification effect. The small focal spot separation results in advantages such as improved stereoscopic image detail, better image quality, and low radiation exposure to the patient.

Longitudinal distortion in images reconstructed by reflection holograms

Reflection holograms recorded on photographic materials usually reconstruct an image at a shorter wavelength than that at which they were recorded. As a result, the lateral and longitudinal magnifications of the reconstructed image are not the same and the image appears distorted. It is shown that this distortion can be minimized by a proper choice of the recording geometry. The residual aberrations of the image are discussed.

Longitudinal magnification in radiologic images of thick objects: a new concept in magnification radiography.

New concepts which are useful for evaluating image resolution and distortion in magnification radiography are introduced. It is shown theoretically and experimentally that "longitudinal magnification" defined as the ratio of the magnified image size to the conventional image size for objects located in a plane perpendicular to the film, is given approximately by the square of the conventional magnification. Resolution in the radiographically magnified image of such objects is much higher than that obtained by optical magnification. This is confirmed experimentally by radiographs of square-wave test objects. The related image distortion is also discussed.

Longitudinal magnification in radiologic images of thick objects: a new concept in magnification radiography

It is common practice to discuss magnification radiography in relation to the magnification of objects located in a plane parallel to the film plane. In this study a new aspect of magnification radiography was introduced which relates to the magnification of objects located in a plane perpendicular to the film plane. This new concept is called the longitudinal magnification. It was shown theoretically that this is approximately equal to the square of the conventional magnification. This is confirmed experimentally from radiographs of square wave test objects. It was shown that this great longitudinal magnification results in image resolution much higher than that obtained by optical magnification. It was concluded that radiographic magnification presents a unique advantage for the imaging of structures located in a plane perpendicular to the film.

Longitudinal Magnification in Radiologic Images of Thick Objects: A New Concept in Magnification Radiography

New concepts which are useful for evaluating image resolution and distortion in magnification radiography are introduced. It is shown theoretically and experimentally that “longitudinal magnification” defined as the ratio of the magnified image size to the conventional image size for objects located in a plane perpendicular to the film, is given approximately by the square of the conventional magnification. Resolution in the radiographically magnified image of such objects is much higher than that obtained by optical magnification. This is confirmed experimentally by radiographs of square-wave test objects. The related image distortion is also discussed.