*3.3. The Photogrammetry Technique*

The photogrammetry measuring method appeared almost simultaneously with the invention of photography. The last few decades have seen the development of digital photogrammetry, which has almost completely replaced analogue photogrammetry in engineering applications. The development of analytical methods has enabled the use of non-metric cameras in engineering applications. The non-metric cameras do not have to strictly meet the requirements for metric cameras, which makes them much cheaper.

In the described case, a Canon 750D digital camera (Oita, Japan) with an 85 mm fixed focus lens was used to make the photograms. The camera was situated on a GigaPano turntable to automatically take the sequences of pictures. The distance from the camera to the tested bridge was 120 m. To verify the assumed method of photogrammetric measurements, a laboratory test was conducted. In the presented case, the lens distortion (with an 85 mm fixed focus lens) was determined based on a photo of 420 mm × 297 mm graph paper on which an ideal grid of squares was applied in AutoCAD (Version 23.0) [29].

The key parameter for photogrammetric measurements is a barrel distortion (Figure 4). This figure shows the image of a square grid deformed by the barrel distortion (red) and the standard square grid (black). Figure 5 shows an image of the camera matrix center. The standard grid of squares (blue) almost perfectly coincides with the symmetry axes of the cropped graph paper. This means that for 1 pixel resolution, any lens errors are imperceptible.

**Figure 4.** The barrel distortion (red) against the background of a standard grid of squares (black).

**Figure 5.** Camera matrix center on the background of the standard square grid (blue).

To verify the quality of the lens, differences (in pixels) between the theoretical (ideal) square grid (created in AutoCAD) and superimposed on the actual image of the square grid (obtained using the tested lens) were measured. The comparison was made in the middle of the outer sides of the frame, where the distortion should be the highest. The basis for determining the amount of distortion was taking a frontal photograph of a sheet of graph paper. Then, the corner image in the pixels was superimposed (shifting along the horizontal line) on the image halfway along the side. The number of pixels extending (in the vertical) beyond the theoretical frame (marked by the blue horizontal line—Figure 6) determines the level of barrel distortion. For the optical system used, the maximum distortion on the upper and lower edges of the frame was 4 pixels (Figure 6a), which means the percentage deformation (2 × 4)/4000 = 0.002, i.e., 0.2%. In other words, the length of the vertical line in the center of the frame is 4008 pixels instead of 4000 pixels, which gives an error of 0.2% ((4008–4000)/4000 = 0.002). One square corresponds to one pixel (Figure 6a). In the analyzed case, the Canon 750D camera matrix has a 22.3 × 14.9 mm physical size and 6000 × 4000 in pixels. The same was done for the shorter edges of the frame, i.e., shifting the corner image along the blue vertical line to the middle of the edge length shows the level of barrel distortion on the short side of the frame. The maximum distortion was 3 pixels (Figure 6b), which means that the percentage deformation is (2 × 3)/6000 = 0.001, i.e., 0.1%. The length of the horizontal line in the center of the frame instead of is 6006 pixels, 6000 pixels, which gives an error of 0.1% ((6006−6000)/6000 = 0.001).

**Figure 6.** Maximum barrel distortion for: (**a**) the upper, (**b**) right edge of the frame, recorded in the middle of its length.

In summary of the lab tests, the registered deformation of the camera-lens system used allows for computerized adjustment with an accuracy of one pixel (Figure 6). Only the central part of the frame (2000/1333 pixels), constituting 1/9 of the entire surface of the frame, was used for the measurement. This is due to use of stitching covering 1/3 of the frame. For the 2000/1333 pixel frame field used, the distortion does not exceed 1 pixel, which is within the interpretational error limit. Therefore, for the expected measurement accuracy and the inability to register deformations in the central part with an accuracy below 1 pixel, it is justified to abandon the calibration procedure.

The AutoPano Giga 4.0 program was applied to process the photograms. The Photoshop CC program (Version 19.0) was applied to calibrate the produced photogram. This was done using a linear rescaling to determine the size of a single pixel.

To receive the bridge deflections at the stage of the dynamic tests, the digital camera was positioned so that it could take a series of photographs at an assumed time, e.g., five photograms per second. As a result, the bridge deflection distributions were measured. To rescale the bridge photograms to the fixed pixel size, the distinctive bridge elements were taken (i.e., the distance between transverse beams of the bridge deck), which were tested earlier using the total station (Figure 3a). The supplementary measurement components, i.e., white reference spheres (Figure 7a) and measuring square shields (Figure 7b), were mounted on the bridge. The photogrammetry technique is characterized by various benefits, such as short measuring time, spatial visualization, and relatively low-cost equipment (digital camera). The results of photogrammetric measurements are dependent mainly on the following determinants:


**Figure 7.** The supplementary measuring components fixed on the structure: (**a**) sphere, (**b**) measuring square shield (checker).
