Many phenomena of interest in nature and industry occur rapidly and are difficult and cost-prohibitive to visualize properly without specialized cameras. Here we describe in detail the virtual frame technique (VFT), a simple, useful, and accessible mode of imaging that increases the frame acquisition rate of any camera by several orders of magnitude by leveraging its dynamic range. The VFT is a powerful tool for capturing rapid phenomena where the dynamics facilitate a transition between two states, and are thus binary. The advantages of the VFT are demonstrated by examining such dynamics in five physical processes at unprecedented rates and spatial resolution: fracture of an elastic solid, wetting of a solid surface, rapid fingerprint reading, peeling of adhesive tape, and impact of an elastic hemisphere on a hard surface. We show that the performance of the VFT exceeds that of any commercial high-speed camera not only in rate of imaging but also in field of view, achieving a 65MHz frame rate at 4MPx resolution. Finally, we discuss the performance of the VFT with several commercially available conventional and high-speed cameras. In principle, modern cell phones can achieve imaging rates of over a million frames per second using the VFT.

Here we have limited the virtual frame rate such that each frame corresponds to approximately one pixel of movement of the front. A higher frame rate is achievable with this data, but not especially useful for the purposes of measuring the front position.

Figures (5)

Fig. 1 Virtual Frame Technique: Schematic Demonstration of Working Principle The dynamics of a v-shaped front propagating at velocity V and traversing the field of view of a camera is shown schematically in both an instantaneous snapshot (a) and a resulting camera image (b), referred to as a Compressed Frame Stack (CFS), recorded with exposure time τ . The grayscale intensity I ( x ) recorded in the CFS is a convolution of the spatio-temporal dynamics of the propagating front, and thus appears blurred. (c) The dynamics are both binary and monotonic, therefore the instantaneous front position can be obtained by deconvolving the compressed frame stack, I ( x ). By way of example, five virtual frames are reconstructed by thresholding I ( x ); these virtual frames correspond to the indicated fractional exposure times t . (d) Two additional hypothetical processes that satisfy the binary and monotonic requirements are shown. The relevant CFS (left) is deconvolved into its constituent virtual frames (right) through thresholding. Note that the dynamics may be evolving in all directions, and from light to dark or vice versa. Download Full Size | PPT Slide | PDF

Fig. 2 VFT and Fast Camera Comparison Using Fracture Dynamics (a) Experimental setup for measurement of a propagating crack tip. A dynamic fracture is initiated in a strained elastomer made of PVS (polyvinyl siloxane). (b) Background lighting and sample opacity were tuned such that the process appears binary at any instant. Two cameras simultaneously record the dynamics such that the crack moves from left to right across both fields of view. Camera one (red) films at 40KHz with a resolution of 320x208 pixels with a total of 60 kilopixels. Six contrast enhanced images from camera one are shown outlined in red. Camera two (purple) films at 5KHz with a resolution of 1280x1000 pixels with a total of nearly 1.3 megapixels; a compressed frame stack is shown outlined in purple at right. The field of view of camera one is superimposed upon the raw image from camera two with a red dashed box. (c) Virtual frames reconstructed from the raw image in (b) are cropped to match the field of view of camera one. The fractional exposure times are chosen such that they correspond to the images recorded by the fast camera in (b). (d) Top: The crack tip location (Δ L ) is measured using both the images of camera one and the virtual frames of camera two. The effective frame rate achieved using VFT is 1MHz, corresponding to β = 200. Because the field of view of the virtual frames is larger than the fast camera frames, the VFT camera (cam two) tracks the crack tip for nearly three times as long as the camera simply filming (cam one). Bottom: A sub-set of the data plotted on a smaller scale highlights the enhanced temporal resolution of the VFT. Full video comparison presented in Visualization 1 . Download Full Size | PPT Slide | PDF

Fig. 3 Wetting Front Propagation Recorded with the VFT a) Experimental and imaging setup. A water droplet impacts a glass prism at velocity V impact . The surface is illuminated in total internal reflection (TIR) using a collimated LED. The reflected light is imaged upon the camera’s sensor using a long-working distance microscope objective. Because a wetted surface is no longer totally internally reflecting, pixels sampling the wetted area appear black. b) A typical compressed frame stack of the TIR signal with V impact = 3.5m/s and exposure time τ = 100 μ s. c) Virtual frames are created by thresholding the compressed frame stack. The small divot at the top of the circular front is an optical aberration. d) Contact radius of many virtual frames vs time. Note that the contact initially spreads at a rate exceeding 50 m/s. The inward-propagating front (bottom) moves much more slowly, at approximately 1.5 m/s. Within the first 5 microseconds of the dynamics, a total of 38 front positions are recorded for a virtual frame rate of nearly 8 MHz. Full video of the dynamics presented in Visualization 2 . Download Full Size | PPT Slide | PDF

Fig. 4 Time-Gated VFT with a ‘Slow’ Camera a) Three experiments - an impacting finger, peeling tape, and an impacting elastic hemisphere - generate compressed frame stacks (CFS’s) using a rectangular light pulse of length 10ms, 1ms, and 250 μ s respectively. The images are taken using the TIR lighting setup shown in Fig. 3 , and have a resolution of 2000x2000 pixels. b) Cropped subsections of the field of view are thresholded to generate virtual frames. Color denotes change from the previous virtual frame. c) Zoom in on fingerprint. Note the contact spreading from many small points to form the larger bands. d) Zoom in on peeling detachment front, Note the cavitation occurring ahead of the front, and the resulting rough contact line. e) Percent contact of the shown subsection over time at 65MHz. Note that this graph represents 1.5% of the field of view and 0.4% of the exposure time. Full videos of the dynamics presented in Visualization 3 , Visualization 4 , and Visualization 5 Download Full Size | PPT Slide | PDF