Untitled

Mak, Se-yuen; Yip, Din-yan

doi:10.1088/0031-9120/36/2/302

Cited by 16 publications

(9 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Second, whatever the result, the mechanism should be investigated by which the process of manufacture reproduces onto the reflecting surface the pattern on the back. (11); this is the sign supported by observation. (b) As (a), but with a < 0, suggested by the stress-release theory but not by observation.…”

Section: Discussionsupporting

confidence: 75%

“…The theory based on the Laplacian image accords well with observation, at least for the mirror studied here. The key insight is that the image of a step is neither a dark line nor a bright line, as sometimes reported [11], but is bright on one side and dark on the other. It is possible that there are different types of magic mirror, where for example the relief is etched directly onto the reflecting surface and protected by a transparent film [11], but these do not seem to be common.…”

Section: Discussionmentioning

confidence: 76%

“…The key insight is that the image of a step is neither a dark line nor a bright line, as sometimes reported [11], but is bright on one side and dark on the other. It is possible that there are different types of magic mirror, where for example the relief is etched directly onto the reflecting surface and protected by a transparent film [11], but these do not seem to be common. Sometimes, the pattern reflected onto a screen is different from that on the back, but this is probably a trick, achieved by attaching a second layer of bronze, differently embossed, to the back of the mirror.…”

Section: Discussionmentioning

confidence: 76%

See 2 more Smart Citations

Oriental magic mirrors and the Laplacian image

Berry

2005

Eur. J. Phys.

View full text Add to dashboard Cite

The pattern embossed on the back of an oriental magic mirror appears in the patch of light projected onto a screen from its apparently featureless reflecting surface. In reality, the embossed pattern is reproduced in low relief on the front, and analysis shows that the projected image results from pre-focal ray deviation. In this interesting regime of geometrical optics, the image intensity is given simply by the Laplacian of the height function of the relief. For patterns consisting of steps, this predicts a characteristic effect, confirmed by observation: the image of each step exhibits a bright line on the low side and a dark line on the high side. Laplacian-image analysis of a magic-mirror image indicates that steps on the reflecting surface are about 400 nm high and laterally smoothed by about 0.5 mm.

show abstract

Section: Discussionsupporting

confidence: 75%

Section: Discussionmentioning

confidence: 76%

Section: Discussionmentioning

confidence: 76%

See 1 more Smart Citation

Oriental magic mirrors and the Laplacian image

Berry

2005

Eur. J. Phys.

View full text Add to dashboard Cite

show abstract

“…Perhaps the earliest example of PCI being put into practice involves the art and demonstration of so-called 'magic mirrors' [5][6][7] that date back to at least the fifth century CE in China and apparently even earlier to the Han Dynasty (206 BCE-24 CE) [7,8], and, the performance of which remained steeped in mystery until the twentieth century. The basic feature of these magic mirrors lay in the fact that a cast or embossed design on the back surface of these bronze mirrors became visible when the highly polished and smooth convex front surface of the mirror was illuminated by direct sunlight and the reflected beam from the front surface of the mirror projected on to a wall.…”

Section: Historical Backgroundmentioning

confidence: 99%

On the evolution and relative merits of hard X-ray phase-contrast imaging methods

Wilkins

Nesterets

Gureyev

et al. 2014

Phil. Trans. R. Soc. A.

141

View full text Add to dashboard Cite

This review provides a brief overview, albeit from a somewhat personal perspective, of the evolution and key features of various hard X-ray phasecontrast imaging (PCI) methods of current interest in connection with translation to a wide range of imaging applications. Although such methods have already found wide-ranging applications using synchrotron sources, application to dynamic studies in a laboratory/clinical context, for example for in vivo imaging, has been slow due to the current limitations in the brilliance of compact laboratory sources and the availability of suitable high-performance X-ray detectors. On the theoretical side, promising new PCI methods are evolving which can record both components of the phase gradient in a single exposure and which can accept a relatively large spectral bandpass. In order to help to identify the most promising paths forward, we make some suggestions as to how the various PCI methods might be compared for performance with a particular view to identifying those which are the most efficient, given the fact that source performance is currently a key limiting factor on the improved performance and applicability of PCI systems, especially in the context of dynamic sample studies. The rapid ongoing development of both suitable improved sources and detectors gives strong encouragement to the view that hard X-ray PCI methods are poised for improved performance and an even wider range of applications in the near future.

show abstract

“…Already 2000 years ago reflectors projecting images, called Chinese magic mirrors, have been hand-crafted of bronze in China and Japan, but the recipe has been lost and reconstructed several times over the ages; see [7] and [46]. Today such free-form optics are important in illumination applications.…”

mentioning

confidence: 99%

Solving the Monge–Ampère equations for the inverse reflector problem

Brix

Hafizogullari

Platen

2015

Math. Models Methods Appl. Sci.

View full text Add to dashboard Cite

The inverse reflector problem arises in geometrical nonimaging optics: Given a light source and a target, the question is how to design a reflecting free-form surface such that a desired light density distribution is generated on the target, e.g., a projected image on a screen. This optical problem can mathematically be understood as a problem of optimal transport and equivalently be expressed by a secondary boundary value problem of the Monge-Ampère equation, which consists of a highly nonlinear partial differential equation of second order and constraints. In our approach the Monge-Ampère equation is numerically solved using a collocation method based on tensor-product B-splines, in which nested iteration techniques are applied to ensure the convergence of the nonlinear solver and to speed up the calculation. In the numerical method special care has to be taken for the constraint: It enters the discrete problem formulation via a Picard-type iteration. Numerical results are presented as well for benchmark problems for the standard Monge-Ampère equation as for the inverse reflector problem for various images. The designed reflector surfaces are validated by a forward simulation using ray tracing.

show abstract

Untitled

Cited by 16 publications

References 4 publications

Oriental magic mirrors and the Laplacian image

Oriental magic mirrors and the Laplacian image

On the evolution and relative merits of hard X-ray phase-contrast imaging methods

Solving the Monge–Ampère equations for the inverse reflector problem

Contact Info

Product

Resources

About