3D Metrology Using One Camera with Rotating Anamorphic Lenses

Abstract

In this paper, a novel 3D metrology method using one camera with rotating anamorphic lenses is presented based on the characteristics of double optical centers for anamorphic imaging. When the anamorphic lens rotates -90° around its optical axis, the 3D data of the measured object can be reconstructed from the two anamorphic images captured before and after the anamorphic rotation. The anamorphic lens imaging model and a polynomial anamorphic distortion model are firstly proposed. Then, a 3D reconstruction model using one camera with rotating anamorphic lenses is presented. Experiments were carried out to validate the proposed method and evaluate its measurement accuracy. Compared with stereo vision, the main advantage of the proposed 3D metrology approach is the simplicity of point matching, which makes it suitable for developing compact sensors for fast 3D measurements, such as car navigation applications.

Keywords: 3D reconstruction; anamorphic lens; anamorphic stereo vision.

Figure 1

Anamorphic imaging model. (a) Imaging rays in the Y_c-O_cy-Z_c plane; (b) imaging rays in the X_c-O_cx-Z_c plane.

Figure 2

The two anamorphic positions. (a) Vertical position and (b) horizontal position which is achieved by a rotation of the anamorphic lens in the vertical position by −90°.

Figure 3

Simulated object points on a spherical surface in anamorphic coordinates of the vertical position.

Figure 4

Simulated image points on the image plane. The dot points refer to the image points when the anamorphic lens is in the vertical position, and the circle points refer to the image points when the anamorphic lens is in the horizontal position.

Figure 5

Simulated image points after anamorphic ration (AR) expansion. The dot points are rectified horizontally by AR, and the circle points are rectified vertically by AR.

Figure 6

Simulated image points tracing from the vertical position to the horizontal position.

Figure 7

Experiment of 3D metrology using rotation anamorphic lenses.

Figure 8

Anamorphic lens composed of a front anamorphic attachment and a rear spherical lens. The anamorphic lens was mounted on a rotary table which could rotate the anamorphic lens by −90° along the optical axis. (a) Side view; (b) Front view.

Figure 9

Anamorphic attachment for a Computar 16 mm spherical lens in the YOZ plane.

Figure 10

Anamorphic images. (a) Image when the anamorphic lens was in the vertical position, and (b) image when the anamorphic lens was in the horizontal position.

Figure 11

Anamorphic images after anamorphic ratio (AR) rectification. (a) Rectified image when the anamorphic lens was in the vertical position, and (b) rectified image when the anamorphic lens was in the horizontal position.

Figure 12

Corners after anamorphic ratio (AR) rectification. The red points indicate the corners in Figure 11a, and the green points indicate the corners in Figure 11b. (a) Image points in their original position, (b) green points shift their positions entirely, after which the two images almost overlap. This pixel decentering was due to the deviation between the optical axis and the axis of the rotary table.

Figure 13

Images for 3D construction when the anamorphic lens was in the vertical position. (a,b) refer to images of 3D targets and (c–h) refer to the images of a 2D target.

Figure 14

Images for 3D construction when the anamorphic lens was in the horizontal position. (a,b) refer to images of 3D targets and (c–h) refer to the images of a 2D target.

Figure 15

Constructed 3D points for images (a–h) in Figure 13 and Figure 14.

Figure 16

Image showing 5000 constructed 3D points for an object point in [500 mm, 500 mm, 1500 mm] with different pixel errors. The standard deviation of the constructed 3D points was 17.3378 mm.

Figure 17

Standard deviation for object points in a plane. The standard deviations for object points with small Y_C coordinates were removed for large reconstruction errors. The standard deviation of the pixel position was 0.2 pixels, the ad was 30 mm, and the Z_C was 1500 mm.

Figure 18

Standard deviation for object points in a plane. The standard deviations for object points with small Y_C coordinates were removed for large reconstruction errors. The standard deviation of the pixel position was 0.2 pixels, the ad was 100 mm, and the Z_C was 1500 mm.