High-sensitivity passive-range metrology

Accurate measurement of distances between objects is required in numerous situations, with examples ranging from assembling and aligning optics to determining the distance to a flag at your local golf course. Both active and passive-range measurement techniques can be used.¹ In active measurement, a local light source projects a beam or a pattern onto the target of interest, and the reflected light is captured by a fixed sensor. For low-range-resolution systems or topographic imaging, the projected beam will produce a geometric pattern onto the target. This is termed the ‘structured-light-system’ approach for ranging.²

Moiré imaging is an example of structured-light projection. Two grid patterns are projected onto the target from different oblique angles, and the morphology of the target's surface can be determined from the overlapping grid patterns. A variation of Moiré imagery uses a mask at the sensor to act as one of the grid patterns.³

In passive ranging, such as parallax or triangulation (see Figure 1), no light source is used to gather information. Two sensors with known separation, Δ, view a specific feature on a distant object. The angles from the sensors to the target feature, α and β, establish the reference coordinate system. The range to this feature, L, can be determined from
                                             
while the change in range is given by
                                                
Eyes determine range this way. Human eyes are separated by approximately 6cm, and the brain is able to interpret the relative rotation of eyes looking at a common object to determine the relative angular difference with an accuracy of approximately 30 arcminutes. Figure 2 shows the absolute and relative human visual-depth resolution as a function of range. A resolution of 1 part in 1000 can be achieved at a distance of approximately 30cm.

Figure 1. Schematic of parallax or triangulation ranging.

Figure 2. The resolution in range sensing that can be achieved by human eyes (left) as a function of object distance and (right) relative to object distance.

We developed a ‘coded target ranging’ approach, where a parallax-based passive variation on structured-light projection is implemented. In the same way that horizontal stripes on a shirt produce an artificial fringe pattern in a video image, an appropriately patterned target will produce an artificial pattern in the ranging camera's images. With a square grid of detector pixels in the focal plane, it is possible to measure very small changes in the distance to an object by placing a pattern on the object, which produces a distance-dependent artificial pattern at the detector.

To demonstrate the system's performance, a camera is set up approximately 1200mm from a target object. A template consisting of a series of bar targets of different scales is fixed to the object and the image is captured. The object is then moved toward the camera and a second image is captured. Figure 3 shows a pair of typical images taken with 1mm difference in object distance. We chose four bar patterns (1 through 4 in Figure 3) for analysis, with the finest pixel sampling (block 4) of approximately 1 pixel per bar or 2 pixels per line pair.

Figure 3. Typical coded target images with 1mm difference in object distance.

Range is determined through the relationship between the real and imaginary parts of the image's modulation transfer function (MTF), which is a mathematical description of the detected pattern. Comparison of the changes in this information as a function of translational position leads to the range-measurement sensitivity. The most sensitive sampling size and corresponding spatial frequency produce the largest ratio of the separation between data sets to the spread within a given data set.

To identify the most sensitive target encoding, we examine the MTF's spatial-frequency information at different target-to-camera separations for the separate bar-target patterns in Figure 3. Figure 4 shows the product of the real and imaginary parts of all spatial frequencies for the detected patterns of targets 2 and 3 at five object distances, separated by intervals of 1mm. Three spatial frequencies in the plot for target 2 show significant magnitude and variability, while for target 3 the most distinctive signature occurs at one particular spatial frequency.

Figure 4. Analysis of the modulation transfer function (MTF)'s spatial-frequency information at all five target-to-camera distances separated by 1mm intervals, for target bar patterns 2 and 3 from Figure 3. The product of the real and imaginary parts of all spatial frequencies for the detected patterns at all object distances are plotted as a function of spatial frequency.

Figure 5 plots the real versus imaginary data clouds to determine the optimum range sensitivity for target 3. To estimate the resolution, note that the angle φ corresponds to a 1mm physical movement and that γ represents the statistical uncertainty in the range measurement at a given position. The ratio γ/φgives the fraction of 1mm that should be resolvable. Dividing this into the 1200mm test separation gives the fractional resolution. In this initial testing exercise, we were able to identify several combinations of bar-pattern sampling and spatial frequencies giving a range-to-resolvable shift exceeding 10,000, with the parameters of Figure 5 achieving 15,000. Future work in this area will center on using this technique to provide real-time configuration monitoring and control of moderate sized structures.

Figure 5. Real versus imaginary MTF data clouds for optimum sensitivity, where the angle φcorresponds to 1mm. The ratio γ/φgives the fraction of 1mm that should be resolvable.