3.1.

Effect of the Distance ($d$)

The effect of the distance between the scan mirror and the cylindrical mirror $d$ was studied with the ZEMAX software for 25.85 and 51.7 mm FL mirrors with an angle $\varphi$ of 45 deg for five different distances of $d$. SR was recorded at five different positions within the 2 mm scan range. In the ZEMAX model, five beam positions with an interval of 0.5 mm were defined within the 2 mm scan range. These scans at positions, indicated by $-1$, $-0.5$, 0, 0.5 and 1 mm, scan are shown in Fig. 3. The results are given in Table 1 for a 51.7 mm FL mirror and Table 2 for a 25.85 mm FL mirror. The simulation results show that, in the case of the 51.7 mm FL, almost the same SR was maintained throughout the 2 mm scan range when the distance between the mirrors $d$ was 50 mm or lower, and if the distance was more than 50 mm, the SR drops slightly towards both ends.

Fig. 3

Five beam positions in the 2 by 2 mm scan field.

Table 1

SR as a function of d’s for a 51.7 mm FL mirror.

Table 2

SR as a function of d’s for a 25.85 mm FL mirror.

In the case of the 25.85 mm FL mirror, a good SR is maintained when the mirror is located at $d$ less than or equal to 25 mm. For a larger distance, the imaging performance drops significantly towards the ends of the scan range. Therefore, to achieve a high imaging quality, the distance between the mirrors should be equal to or less than the FL of the mirror. However, due to the experimental constraints, the distance between the mirrors $d$ of 35 mm was used for experiments.

3.2.

Effect of the Incident Angle ($\varphi$)

Table 3 shows the value of the parameters that were used in the ZEMAX model to evaluate the effect of the incident angle. The optical scan angle from the ZEMAX and the angular variations ($\varphi \pm \theta /2$) for 51.7 and 25.85 mm FL mirrors with different $\varphi$ are given in Table 4. Here, the optical scan or the angular variation corresponds to the 2 mm scan range for a defined $\varphi$.

Table 3

ZEMAX model parameters.

Table 4

Angular variations simulated using the ZEMAX for a 2 mm scan range.

The EFL was optimized with a different angle of $\varphi$ for the best SR within the 2 mm scan range. The optimized EFL positions of the 51.7 and the 25.85 mm FL mirror are given in Table 5. Figure 4(a) shows the SR comparisons with these incident angles for a 51.7 mm FL mirror, and Fig. 4(b) shows the SR comparisons for a 25.85 mm FL mirror at optimized EFL for the specific $\varphi$. In the case of the 51.7 mm FL mirror, the SR remained better than the Marechal criteria throughout the 2 mm scan range regardless of the angle $\varphi$. In the case of the 25.85 mm FL mirror, the SR was higher than the Marechal criteria throughout the 2 mm scan range when the incident angle was 30 deg. However, in the case of the 45 and 60 deg angles, the SR drops towards both ends of the 2 mm scan range. The SR drops because a higher optical angle is required when using a lower FL mirror to scan the same 2 mm range.

Fig. 4

SR comparisons at different incident angles using (a) a 51.7 mm FL mirror and (b) a 25.85 mm FL mirror.

Table 5

Optimized EFLs with different ϕ.

The model was optimized for a best SR for each beam position within the 2 mm scan range. The EFL position was optimized individually for five different beam positions. The EFL position variations with different incident angles for 51.7 and 25.85 mm FL mirror are shown in Fig. 5(a) and 5(b), respectively. The results show that the variation of the EFL position ($\mathrm{\Delta }\mathrm{EFL}$) is higher when reducing the FL of the mirror and/or increasing the angle between the incident and reflected beams. For example in the case of the 51.7 mm FL mirror, ΔEFL is 250 μm from the center to one end of the scan field with $\varphi =60\mathrm{deg}$ compared to a $\mathrm{\Delta }\mathrm{EFL}$ of 50 μm with $\varphi =30\mathrm{deg}$. Similarly at $\varphi =60\mathrm{deg}$ the $\mathrm{\Delta }\mathrm{EFL}$ varies from 250 to 874 μm if the FL of the mirror is changed from 51.7 to 25.4 mm. Because of this higher ΔEFL, the imaging quality drops significantly towards the ends of the scan field. In order to obtain high imaging quality, the angle between the incident and reflected beams $\varphi$ should be 0 deg making it anon-axis scanning system. Since this is not possible, flat scan field can be achieved by using an angle $\varphi$, which is as low as the design would permit.

Fig. 5

EFL position variations at different incident angles with (a) a 51.7 mm FL mirror and (b) a 25.85 mm FL mirror.

5.1.

Flatness Evaluation With Y-Scan System Configuration

In the Y-scan configuration, the collimated beam was focused in the Y-axis while the X-axis remained the same as the collimated beam size. The system parameters that were discussed in Sec. 3 were used for the experiments. The scanning was performed by rotating the scanning mirror in the Y-axis. Five beam profiles were captured with an interval of 0.5 mm within the 2 mm scan range. The experiments were repeated for the incident angles of 30, 45, and 60 deg with a distance of $d=35\mathrm{mm}$. Comparisons of SR between ZEMAX modeling and the experiments for a 51.7 mm FL mirror, with the beam positons set at incident angles of 30, 45, and 60 deg are shown in Fig. 7(a) to 7(c), respectively. In the case of 30 and 45 deg incident angles, the SR remained above the Marechal criteria throughout the 2 mm scan range. In the case of the 60 deg incident angle, the SR is 2.5% lower than the Marechal criteria at one end of the 2 mm scan range.

Fig. 7

SR comparison of 51.7 mm FL mirror with the angle of (a) $\varphi =30\mathrm{deg}$ (b) $\varphi =45\mathrm{deg}$, and (c) $\varphi =60\mathrm{deg}$.

Because of the off-axis configuration, the beam is blocked by the camera housing for $\varphi <45\mathrm{deg}$ with a 25.85 mm FL. Thus, the experiments were restricted to $\varphi <45\mathrm{deg}$ and $\varphi <60\mathrm{deg}$ with a 25.85 mm FL. In the case of shorter FL mirrors, a larger optical scan angle was required to scan the 2 mm scan range compared to that of the longer FL mirrors, resulting in increased EFL position variations. The model results and the experimental results with 45 and 60 deg angles are shown in Fig. 8(a) and 8(b), respectively. In the case of 45 deg angle, the variation between model and experimental measurements is 29% whereas this variation is 39% in the case of 60 deg angle. However, with the different incident angle the result shows the same trend within the scan range. The modeling results in Sec. 3 show that the scanning system maintained a consistent SR within the 2 mm scans range with an angle of $\varphi =30\mathrm{deg}$. Therefore, variations of the imaging quality can be reduced by using a lower angle of $\varphi$, as discussed in Sec. 3.2.

Fig. 8

SR comparison for 25.85 mm FL mirror with the angle of (a) $\varphi =45\mathrm{deg}$ and (b) $\varphi =60\mathrm{deg}$.

The experiments were performed in a free space optics system, where the system geometric parameters such as the distance $d$, the angle $\varphi$ and the $r$, were restricted by the size of the optics and that of the CCD camera. However, in the real imaging system, scanning would be performed on the sample instead of on the CCD camera, and the scanning mirror can be replaced by a MEMS mirror. Design of a miniature scanning system was reported in our earlier work.¹⁵ The mirror distance of $d=10\mathrm{mm}$ and the angle of $\theta =20\mathrm{deg}$ with the 14.95 mm FL mirror were used in the miniature scanning system simulation. With these parameters, the scanning system maintained an SR more than 0.97 throughout the 2 mm scan range. Therefore, the developed scanning can be used in endoscopic OCT imaging as well as in external OCT imaging applications with a higher transverse resolution.

5.2.

Flatness Evaluation with X-Scan System Configuration

X-scanning was performed to evaluate the effect of the scanning direction on the flatness of the scan field. The ZEMAX optical design software does not permit changing the scanning as well as the focusing direction for this off-axis scanning system configuration. Thus, the flatness of the scan field was experimentally evaluated by using an X-scan. For this set of experiments, same system parameters that were used in the optical model and in the Y-scan configuration were repeated. X-scans were performed by changing the focusing and the scanning direction from the Y-axis to the X-axis. When the scanning direction was changed from Y to X, the scanning was performed in the orthogonal plane with respect to the incident beam. Because of that the incident angle $\varphi$ does not have any influence on the angular variations during the scanning. Hence, the EFL positions vary as a function of the scan angle. The incident angles of 30, 45 and 60 deg were used with the 51.7 mm FL mirror. Because of the experimental constraints, in the case of the 25.85 mm FL mirror, the experiments were limited to the incident angles of 45 and 60 deg. Experiments were performed by positioning the beam at the center C of the mirrors. Five beam profiles were captured within the 2 mm scan range, and then the profiles were processed to extract the SR value. Comparisons of the SR for the beam position at C are shown in Fig. 9(a) and 9(b) for the 51.7 mm FL mirror and for the 25.85 mm FL mirror, respectively. The experimental results show that the SR maintained above the Marechal criteria of 0.8 throughout the 2 mm scan range regardless of the focal length and the incident angle.

Fig. 9

X-scan SR comparison with the beam position at $C$ for (a) 51.7 mm, and (b) 25.85 mm FL mirror.

Two off-set positions on the cylindrical mirrors were used to evaluate the sensitivity of the scanning system to variations in beam positioning. For both mirrors, a 1 mm off-set from the center ($C+1$) and a 2 mm off-set from the center ($C+2$) were studied. Five beam profiles were recorded within the 2 mm scan range for each off-set position. The SR comparisons of these beam positions are shown in Figs. 10 and 11, respectively. Experimental results show that the SR maintained above the Marechal criterion throughout the 2 mm scan range regardless of the beam position, the incident angle, and the radius of curvatures. Therefore, the developed scanning system provides flat scan field by maintaining consistent SRs throughout the 2 mm scan range.

Fig. 10

X-scan SR comparison with the beam position at $C+1$ for (a) a 51.7 mm FL mirror and (b) 25.85 mm FL mirror.

Fig. 11

X-scan SR comparison with the beam position at $C+2$ for (a) 51.7 mm FL mirror and (b) 25.85 mm FL mirror.

3-D beam profiles from the Y-scan and from the X-scan made by using a 51.7 mm FL mirror and a 25.85 mm FL mirror are shown in Figs. 12 and 13, respectively. In the case of the 51.7 mm FL mirror, the beam profiles show consistency throughout the 2 mm scan range in both scanning directions. In the case of the 25.85 mm FL mirror, the beam profile lost consistency towards the ends of the 2 mm scan range when using the Y-scan system configuration. The reason for this loss is attributed to the higher angular variation with respect to the angle between the incident and the reflected beam for the same scan field of 2 mm. In the case of the X-scan system configuration, the beam profiles maintained consistency throughout the 2 mm scan range. In this configuration, the scanning was performed in the orthogonal plane with respect to the incident beam. Therefore, the incident angle does not have any impact on the angular variation.

Fig. 12

3-D map of 51.7 mm FL mirror with $\varphi =60\mathrm{deg}$ (a) Y-scan and (b) X-scan configuration.

Fig. 13

3-D map of 25.85 mm FL mirror with $\varphi =60\mathrm{deg}$ (a) Y-scan and (b) X-scan configuration.

5.3.

Transverse Resolution Comparison

The shape and the size of the spread function determine the transverse resolution. Imaging quality depends on the consistency of the transverse resolution throughout the scan range. Transverse resolution in the line focusing direction is quantified by using FWHM of the spread function. Therefore, a consistent FWHM is required to achieve a flat scan field image. To evaluate the effect of the scan direction on the FWHM, the spread function was extracted from five beam profiles. Figure 14 shows the spread function at five scan positions within a 2 mm scan range using the 25.85 mm FL mirror at the angle $\varphi =45\mathrm{deg}$. In the case of the X-scan, a 15 μm transverse resolution is maintained throughout the 2 mm scan range. In the case of the Y-scan, a 15 μm transverse resolution was achieved only at the center of the scan field. It drops significantly towards the ends of the scan field.

Fig. 14

X-scan and Y-scan transverse resolution within 2 mm scan range at different scan position.