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Experiments on Calibrating Tilt-Shift Lenses for Close-Range Photogrammetry

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Experiments on Calibrating Tilt-Shift Lenses for Close-Range Photogrammetry The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016 XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic EXPERIMENTS ON CALIBRATING TILT-SHIFT LENSES FOR CLOSE-RANGE PHOTOGRAMMETRY E. Nocerino a, *, F. Menna a, F. Remondino a, J.-A. Beraldin b, L. Cournoyer b, G. Reain b a 3D Optical Metrology (3DOM) unit, Bruno Kessler Foundation (FBK), Trento, Italy – Email: (nocerino, fmenna, remondino)@fbk.eu, Web: http://3dom.fbk.eu b National Research Council, Ottawa, K1A 0R6, Canada – Email: (Angelo.Beraldin, Luc.Cournoyer, Greg.Reain)@nrc-cnrc.gc.ca Commission V, WG 1 KEY WORDS: Tilt-shift lens, Scheimpflug principle, Close range photogrammetry, Brown model, Pinhole camera, Calibration, Accuracy, Precision, Relative accuracy ABSTRACT: One of the strongest limiting factors in close range photogrammetry (CRP) is the depth of field (DOF), especially at very small object distance. When using standard digital cameras and lens, for a specific camera – lens combination, the only way to control the extent of the zone of sharp focus in object space is to reduce the aperture of the lens. However, this strategy is often not sufficient; moreover, in many cases it is not fully advisable. In fact, when the aperture is closed down, images lose sharpness because of diffraction. Furthermore, the exposure time must be lowered (susceptibility to vibrations) and the ISO increased (electronic noise may increase). In order to adapt the shape of the DOF to the subject of interest, the Scheimpflug rule is to be applied, requiring that the optical axis must be no longer perpendicular to the image plane. Nowadays, specific lenses exist that allow inclining the optical axis to modify the DOF: they are called tilt-shift lenses. In this paper, an investigation on the applicability of the classic photogrammetric model (pinhole camera coupled with Brown’s distortion model) to these lenses is presented. Tests were carried out in an environmentally controlled metrology laboratory at the National Research Council (NRC) Canada and the results are hereafter described in detail. 1. INTRODUCTION image plane. Camera movements are possible when using view or technical cameras, which are large format cameras where the Close-range photogrammetry (CRP) is a powerful technology lens, usually mounted on a folding baseboard or a monorail because of its flexibility for speedy reconfiguration and the (Figure 1a), projects the image on a ground glass to allow for possibility to accomplish very demanding tasks while keeping focusing. Once the focus is set, the ground glass is replaced by the costs reasonable. It is an established technology worldwide the film holder. View cameras are mainly used by professional for 3D recording in industrial/engineering as well as in cultural photographers in studio or for architectural photography. Even if heritage applications. Nevertheless, when the imaging distance is adapters are now available for digital single-lens reflex (DSLR) small (less than 2 m), the depth of field (DOF), i.e. the axial cameras (Figure 1b), these systems are not very suitable for (longitudinal) resolving power of the employed optical system, photogrammetry due to their low flexibility and portability. A becomes a strong limiting factor. DOF extends in front of the more practicable solution is represented by tilt-shift lenses camera and can be visualized as a prism with two faces parallel (Figure 1c), also called perspective control (PC) lenses, which to the sensor plane. The portion of object that falls into the solid are available for smaller camera format (e.g., 35 mm or full will be rendered adequately sharp, or in other words with enough frame) and allow for some of the view camera movements. In detail in the image. particular, by rotating the tilt-shift lens of a proper angle, an A way for controlling and adapting the DOF to the scene of inclined subject may be fitted within the optical system DOF, interest is to use the so called camera movements (Ray, 2002), according to the Scheimpflug rule. i.e. translational and rotational movements both of the lens and a) b) c) Figure 1. a) Linhof Kardan E view camera (http://www.fotografie-boerse.de/angebote_30_4/). b) Cambo Ultima 35: adapter for DSLR cameras (https://cambouk.wordpress.com/2013/09/26/cambo-special-offer-ultima-35-camera-bundles/). c) DSRL camera (Nikon D750) with a tilt-shift lens (PC-E Micro NIKKOR 45mm f/2.8D ED). * Corresponding author This contribution has been peer-reviewed. doi:10.5194/isprsarchives-XLI-B5-99-2016 99 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016 XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic This paper presents the first results of a wide experimental study (Figure 2). The concept of COC goes back to analogue conducted in an environmentally controlled metrology laboratory photography and to the printing and enlargement (or at the National Research Council (NRC) Canada to investigate magnification) of film. The value of COC or blur circle is the metric capability and benefits of tilt-shift lenses. Several originally defined according to the finer detail that is visible by experiments evaluated the overall performance of a DSLR human eye at a comfortable vision distance on a printed and camera equipped with a tilt-shift lens, using quality parameters magnified photograph. It depends on the camera format and lens for measurement uncertainties, i.e. accuracy and precision. To used. COC typical values for different analogue camera formats rigorously model the image formation when the Scheimpflug are provided in Ray (2002). For digital cameras, COC is usually principle is employed, the actual angle between the optical axis taken as around 1-3 pixels (Menna et al., 2012; Luhmann et al., and the image plane should be included in the mathematical 2014). formulation. Neglecting this angle would certainly introduce systematic errors in the photogrammetric measurement process. Nevertheless, if this angle is bounded to a range of ±4 degrees for most practical uses, the error introduced might be limited and compensated by calibration parameters. Such evaluation has not been done until now and therefore the present investigation aims at evaluating if the most popular photogrammetric model, i.e. the pinhole camera coupled with Brown’s formulation for lens distortion, can be considered still valid for tilt-shift lenses and to Figure 2. COC and DOF for a lens focused at finite distance. which extent. The rest of the paper is structured as follows. Section 2 reports According to Ray (2002, page 218), DOF can be computed the motivations behind the study, along with a discussion on according to equation (1): DOF, Scheimpflug condition and tilt-shift lenses. Section 3 presents the experiments, with particular emphasis on the 퐷푂퐹 = 퐹푎푟푃푙푎푛푒 − 푁푒푎푟푃푙푎푛푒 2 2 photographic equipment, the calibration fixture specifically 2 ∙ 푓 ∙ 퐷 ∙ 퐹푛푢푚푏푒푟 ∙ 퐶푂퐶 (1) = designed for the tests and the acquisition protocol adopted. 4 2 2 2 푓 − 퐹푛푢푚푏푒푟 ∙ 퐶푂퐶 ∙ 퐷 Finally (Section 4), the results of the experimental investigation are presented and discussed. where: - 퐹푎푟푃푙푎푛푒 and 푁푒푎푟푃푙푎푛푒 are the far and near limits of 2. MOTIVATION AND BACKGROUND DOF, respectively; - 푓 is the lens focal length; The aim of the collaborative research between FBK and NRC is - 퐷 is the focusing distance; to explore the use of Scheimpflug rule, a well-known principle - 퐹푛푢푚푏푒푟 is lens relative aperture. commonly exploited in “artistic” and professional photography For large object distance, equation (1) can be simplified to (Ray, (Merklinger, 1996; Evens, 2008) as well as active triangulation 2002; Luhmann et al., 2014): scanning technique (Dremel et al., 1986; Rioux et al., 1987; 2 2 Albers et al., 2015) and particle image velocimetry – PIV 퐷푂퐹 ≈ (2 ∙ 퐷 ∙ 퐹푛푢푚푏푒푟 ∙ 퐶푂퐶)⁄푓 (2) (Fournel et al., 2004; Louhichi et al., 2007; Astarita, 2012; Hamrouni et al., 2012), but not yet adequately investigated in In this case, it can be easily argued that the DOF increases with CRP. the COC, the f-number and the square of focusing distance, while decreases when the focal length grows. When working in close 2.1 DOF and Scheimpflug rule up photogrammetry, which corresponds typically to a magnification1 range of 0.1-1 and object distance range of 1000 DOF is the distance between the nearest and farthest object mm - 10 mm (Ray, 2002), DOF is very limited. planes still in focus, i.e. the distance between the nearest and In an ordinary camera setup, the points in space that are in focus farthest objects in a scene that appear acceptably sharp in an ideally lie in a plane parallel to the image plane and, once decided image. Sharpness can be defined as the quality for which the focal length, the desired DOF is generally accomplished adequate resolved details and, hence, information content, are changing the f-stop value. A smaller aperture yields a greater provided by the image. In absence of other degrading factors DOF but may lead to diffraction that in turn leads to a loss of (aberrations, camera shake, etc.) sharpness only depends on image detail (Luhmann et al., 2014). In CRP, usually the objects correctly focusing the subject of interest. From a physical point to be surveyed are three-dimensional and of varying depth, but a of view, a lens can precisely focus at only one distance: there perfectly sharp image is obtained only for the part of the object exists only one specific distance where a point in object space is that is within the DOF. According to the Scheimpflug rule, by imaged in the image plane as a sharp point. At any other tilting the lens so that its axis is no longer perpendicular to the distances, an object point produces a blur circular spot, which plane of the sensitive media, film or digital sensor (Figure 3), the means that the point is defocused.
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