# Visualizing Small Objects Using Amplitude-Modulated Laser Light at Microwave Frequencies
## 4 Experimental Results and Comparison between Two Experiments  
### Results of the LADAR Experiment  
First, we describe the results that were obtained by the fixed-target-position measurements using the settings depicted in Figure 3a. The laser light was spotted on the sphere with a diameter of \(94\) mm. The spot size was \(7\) mm. Figure 5a,b shows that the scattered light from the front area within a diameter of \(40\) mm can be detected well. The scattered light intensity falls sharply outside of this area. The phases of the detected signals, \(\varphi\), in the scanned area are shown in Figure 5c,d. The scattering point positions were found with the aid of \(\varphi=j2\mathbf{k}\cdot\mathbf{r}_{l}\). We confirmed that the phase within the diameter of \(40\) mm showed a smooth decline. In Figure 6 the range, i.e., the position of the light scattering, is plotted by a blue line on the horizontal line that passes through the center of the sphere.  
Figure 4: Top view of synthetic aperture experiment setup. The interference signals, \(F(\mathbf{k})\), were collected as a function of the stage rotation angle and the chirped microwave frequency.  
Figure 3: **(a)** Block diagram of the LADAR system. The laser, which is amplitude-modulated at the FM microwave frequencies, was spatially scanned on the surface of the target. **(b)** Picture of the spherical target with diameter of \(94\) mm, which was covered by reflective paint.  
The blue dotted line and the yellow line denote the fitting curve using a quadratic function applied to the measurement results and real shape of the spherical target. The range values of the fitting and the real curves were almost consistent with each other within the 40 mm diameter. On the other side, the range value difference between them gradually increased toward the edge. We considered that this was caused by the finite spot size (7 mm) of the projection laser beam on the cross-range plane. The laser beam projected a small finite area on the target surface. In such a situation, the measured phase value is mainly considered to result from reflected waves with a large amplitude. Thus, the range measured with the phase likely corresponds to a target with a high backward cross-section in the projected area. Since the cross-section outside of the 40 mm diameter  
Figure 5: Image of the sphere obtained by the fixed target measurements: (**a**) the 2D amplitude image; (**b**) the 3D amplitude image; (**c**) the 2D phase image; (**d**) the 3D phase image.  
Figure 6: Range image of the sphere extracted on the horizontal axis from Figure 3b is plotted by thick blue curve. Blue dotted curve denotes the observed fitting curve. Orange curve denotes the actual shape of the sphere.  
began to sharply decrease as shown in Figure 5b, phase values measured in the edge region would be strongly affected by the position closer to the center within the projected footprint of the laser. On the other side, the backward cross-section near center was almost flat, and average of the range inside the footprint was measured. Thus, from the measured cross-range error of the edge measurements, cross-range resolution was estimated to be about 7 mm, which is equal to the beam spot size. The measured range was fluctuating as shown in the blue solid curve in Figure 6. This fluctuation is dealt as a range resolution. The range resolution seemed to be depending on detected power at each measurement position, as studied in detail on the reference [10]. We did not perform detailed research on this relationship, however, brief analysis from Figures 5 and 6 was as follows. The signal to noise ratio (SNR) could be estimated from Figure 5b. The detected power level measured over 40 mm of the horizontal position did not change, thus, was thought to be a noise floor level. The SNR evaluated at 20 mm (center of the sphere), 35 mm, and 45 mm (edge) were over 100, 10, and 1, respectively. The range resolutions at corresponding positions were about 0.2 mm, 1 mm, and 5 mm, respectively; which was improving as increasing in the SNR.