Multi-pulse time delay integration method for flexible 3D super-resolution range-gated imaging

Wang Xinwei; Li Youfu; Zhou Yan

doi:10.1364/OE.23.007820

1. Introduction

Three-dimensional super-resolution range-gated imaging (SRGI) is a novel 3D flash imaging technique developed in 2007 [1]. This technique is realized by the range-intensity correlation of range-intensity profiles (RIP) between overlapped gate images. The term super-resolution refers to the range resolution far beyond the classical resolution limitation of 3D range-gated imaging based on time slicing [2, 3]. 3D SRGI uses the specific shape of range-intensity profiles to extract range information. Up to now, the 3D reconstruction algorithms have been developed by two approaches. One is based on gate images with trapezoidal RIPs [1], and the other is based on gated images with triangular RIPs [4].

To obtain regular triangular or trapezoidal RIPs, the illuminator laser pulse and sensor gate pulses must be rectangular shaped. Typically, a CCD with a gated image intensifier (i.e. ICCD) is used as the image sensor in a 3D range-gated imaging system where the image intensifier acts as a shutter gate. The gate time of the current state-of-the-art ICCD can reach ps level. Because the scale of gate time is typical ns or μs level in 3D SRGI [1, 4–7], the gate sensor of ICCD can generate desired rectangular gate pulse with ns- or μs-scale gate time. The illuminators utilized in range-gated imaging are laser diode and solid-sate laser. For the laser diodes, the laser center wavelength is typical 808nm or 860nm, and the laser pulse width varies from dozens of ns to several μs with rectangular or quasi-rectangular pulse shape [1, 4–6, 8]. Currently, laser diodes are also widely used as illuminators for 3D SRGI [1, 4–6]. However, the near-infrared range-gated imaging systems are only performed during evening because during daytime the daylight dominates over the laser illumination, and they are also not suitable for underwater imaging due to large water attention. Therefore, 532nm and eye-safe 1.5μm solid-state lasers are implemented as illuminators respectively for underwater imaging [3, 7] and all-day imaging in different atmospheric conditions [9–12]. However, the pulse width of solid-sate laser is relatively constant. In 3D SRGI, the depth of 3D imaging is determined by laser pulse width, and thus the constant pulse width results in fixed depth of 3D imaging. If the depth of viewing is fixed, especially for a small value, 3D SRGI is faced with the 3D imaging failure due to the positioning uncertainty of the imaging zone with regard to the searched targets. What’s worse, for a large depth of 3D imaging one must scan the targeted scene as illustrated in Fig. 1, and correspondingly large raw data volume generates. Obviously, this scanning way reduces the real time performance of 3D SRGI. In addition, the other drawback of solid-state lasers is that the laser pulse shape is not rectangular but Gaussian or quasi-Gaussian so that regular triangular or trapezoidal RIPs cannot be obtained for 3D SRGI. The mismatch with the specific shape of RIPs also leads to the failure of 3D SRGI.

Fig. 1 Depth scanning of 3D SRGI for large depth of viewing. (a) Target scene. (b) Scanning under the triangular algorithm. (c) Scanning under the trapezoidal algorithm.

Download Full Size | PDF

To flexibly adjust the depth of 3D imaging and establish desired RIPs with specific shapes based on solid-state lasers, a multi-pulse time delay integration (MPTDI) method is proposed in this paper. This paper is structured as follows. In Section 2, the principle of MPTDI is introduced. In the next section, an equivalent model of laser pulse temporal shaping is established for MPTDI, and the characteristics of the equivalent output laser pulse are analyzed by the model. In Section 4, two typical RIPs with triangular and trapezoidal shapes are established and discussed. In Section 5, the experiments of 3D SRGI based on MPTDI are performed and discussed under the triangular correlation algorithm. Finally, we conclude the MPTDI method.

2. Multi-pulse time delay integration method

The principle of multi-pulse time delay integration method is illustrated in Fig. 2. Similar to a traditional range-gated imaging system, the range-gated imaging system utilizing MPTDI consists of a pulsed laser, a gated ICCD and a time control unit. In the method, a ps- or ns-scale pulsed laser is implemented with a high pulse repetition frequency, and thus the laser can be split into many laser pulses in time domain as shown in Fig. 2 (a). Every laser pulse is convoluted with a gate pulse at a predetermined time delay to yield a sub-RIP. Different sub-RIPs have different time delay, and thus different sub-RIPs correspond to different sampling zones. Finally, all the sub-RIPs are integrated on the CCD chip and generate a gate image with a desired target RIP. The time sequence of MPTDI is depicted in Fig. 2(b) where a laser pulse and a gate pulse form a pulse pair. Different pulse pairs have different time delay, and the time delay of the i^th pulse pair is τ_i = τ₁ + (i-1)δt, where τ₁ is the initial time delay of the first pulse pair, i is the pulse pair number, and δt is the delay step. A pulse pair generates a sub-frame with a fixed sub-RIP determined by the convolution of a laser pulse and a gate pulse. The sub-RIP location of the i^th sub-frame is determined by τ_i as R_sub,i = τ_ic/2 where c is the light speed. When the laser pulse width is t_l and the gate time is t_g, the depth of a sub-frame is d = (t_l + t_g)c/2. All sub-frames generated by pulse pairs are integrated in a single CCD frame. This process is intra-frame integration where no new frame is yielded. Therefore, the integration has no influence on the real-time acquisition of gate images. For a gate image outputted under MPTDI the complete description of the integration reflectivity energy is given by

E (r) = N \sum_{i = 1}^{M} E_{s u b . i} (r)

where r is the target range, M is the total number of pulse pairs in an integration group, N is the total number of the integration groups in a single frame, and E_sub,i is the reflectivity energy of the i^th sub-frame. Typically, M and N meet N = ⌊ f _PRFt_e/M⌋ where ⌊⌋ stands for rounding down to the nearest whole number, f_PRF is the laser pulse repetition frequency, and t_e is the exposure time of a single CCD frame. This equation is referred to as an integration of a series of individual convolutions between the laser pulses and the gate pulses within a projected sensor pixel. E_sub,i is given as

E_{s u b . i} (r) = \int_{0}^{\infty} P (t - 2 r / c) G (t - τ_{i}) d t

where P(t) and G(t) are the laser pulse and gate pulse functions respectively, and c is the light speed. In Eq. (2), the atmospheric attenuation and other temporal and spatial factors such as laser beam divergence, target reflection property and pulse repetition frequency are neglected, because they are all eliminated in the formulas of extracting target range information in 3D SRGI [1,4].

Fig. 2 Multi-pulse time delay integration method. (a) Principle. (b) Time sequence. (c) Integrated RIP.

Download Full Size | PDF

Under the MPTDI shaping method, the RIP of a gate image is illustrated in Fig. 2(c). All gate images yielded by MPTDI have the same features with traditional gate images. In MPTDI, the location of the gate image is

R = \frac{τ c}{2}

where τ is the equivalent time delay and is determined as τ = τ_i + (M-i)δt.

The equivalent gate time is

t_{G} = t_{g}

The equivalent laser pulse width is

t_{L} = t_{l} + (M - 1) δ t

In MPTDI, the depth of RIP is D = (t_L + t_G)c/2. When t_G>t_L the RIP shape is a trapezoid, and when t_G = t_L the RIP shape is a triangle. Here Fig. 2(c) only shows the trapezoidal case. In Fig. 2(c), the RIP includes a head, a body and a tail. The head and tail have the same depth of t_Lc/2. The depth of the body is (t_G-t_L) c/2. For the triangular case, the RIP only includes a head and a tail without a body, and the head and tail also have the same depth of t_Lc/2. Obviously, the RIP shape can be changed by matching the equivalent laser pulse width with the equivalent gate time in terms of Eqs. (4) and (5).

3. Laser pulse temporal shaping model for MPTDI

The MPTDI method constructs desirable RIPs by integrating of multiple sub-RIPs. However, the time delay integration process is complex and cannot directly exhibit the relationship between the input laser pulses and the gate image RIP characteristics. To solve this problem, an equivalent model is established in this section.

In terms of Eq. (2), Eq. (1) can be further deduced as

\begin{array}{l} E (r) = N \sum_{i = 1}^{M} \int_{0}^{\infty} P (t - 2 r / c) G (t - τ_{i}) d t \\ \begin{matrix}  \end{matrix} = N \int_{0}^{\infty} P (t - 2 r / c) [\sum_{i = 1}^{M} G (t - τ_{i})] d t \\ \begin{matrix}  \end{matrix} = N \int_{0}^{\infty} [\sum_{i = 1}^{M} P (t - (M - i) δ t - 2 r / c)] G (t - τ) d t \\ \begin{matrix}  \end{matrix} = N \int_{0}^{\infty} P_{o u t p u t} (t - 2 r / c) G (t - τ) d t \end{array}

where P_output(t) is the function of the output laser pulse which is reshaped by the temporal shaper as

P_{o u t p u t} (t) = \sum_{i = 1}^{M} P (t - (M - i) δ t)

Equation (7) demonstrates that the MPTDI method can be simplified as a laser pulse temporal shaping model where the time delay integration of M-pulse-pair convolution is equivalent to the convolution of a gate pulse with an equivalent output laser pulse integrated by M input laser pulses. By integrating finite-width input laser pulses side by side, an equivalent output laser pulse is generated as shown in Fig. 3.

Fig. 3 Equivalent output laser pulse by integrating M input laser pulses.

Download Full Size | PDF

To evaluate the uniformity and rectangular features of the output laser pulse, the rectangular coefficient of ξ is defined as

ξ = U S

where U is the flat-top uniformity of the output laser pulse profile, and S is the shape factor. They are respectively defined as

U = \frac{P_{v a l l e y}}{P_{p e a k}}

S = \frac{t_{t o p}}{t_{b o t t o m}}

where P_valley and P_peak are the valley and peak power in the quasi flat-top region, t_top and t_bottom are the top width and the bottom width of the output laser pulse.

The flat-top uniformity of the output laser pulse is related to the uniformity coefficient that is defined as

u = \frac{δ t}{t_{l}}

where δt is the delay step between laser pulses. Equation (5) is still available in the laser pulse temporal shaping model. Referring to the definition of the uniformity coefficient, the output laser pulse width is

t_{L} = (M u - u + 1) t_{l}

Equation (12) demonstrates that although for a pulsed solid-state laser the laser pulse width of t_l is constant, the output laser pulse width can be adjusted by changing the input laser pulse number and the uniformity coefficient.

4. Uniformity and rectangular characteristics of output laser pulses

The accumulation of multiple sub-RIPs can be equivalent to the convolution of an equivalent output laser pulse with a gate pulse. The characteristics of the output laser pulse determine the RIP shape. In this section, the uniformity and rectangular properties of the output laser pulse profile will be discussed in advance to support the following discussion of Section 5.

Generally, a laser pulse temporal shape can be regarded as a Gaussian or quasi-Gaussian shape [2, 13, 14]. A Gaussian shape follows P(t) = P₀/(2πt_HW1/e)^1/2exp[-t²/(2t_HW1/e²)], where P₀ is the peak power of the laser pulse, and t_HW1/e is the half width when the pulse intensity decrease to 1/e of its maximum. In Sections 2 and 3, t_l mentioned is the full width half maximum (FWHM). The relationship between t_l and t_HW1/e is t_l = 2(ln2)^1/2 t_HW1/e. For a quasi-Gaussian pulse, it is typically given as P(t) = (t/t₀)²exp(-t/t₀) where t₀ = t_l/3.5. Figure 4 gives the simulation results under the two types of input laser pulses. Figure 4(a) shows the output laser pulse profiles by integrating multiple Gaussian laser pulses, and Fig. 4(b) shows the profiles by integrating multiple quasi-Gaussian laser pulses. In the simulation, the target laser pulse has a rectangular shape with a laser pulse width of 100ns, the Gaussian and quasi-Gaussian input laser pulses have the same FWHM of 4ns, and the uniformity coefficient and input laser pulse number are given in Table 1.

Fig. 4 Output laser pulse profiles under different uniformity coefficients. (a) Output laser pulse profiles integrated by Gaussian input laser pulses. (b) Output laser pulse profiles integrated by quasi-Gaussian input laser pulses.

Download Full Size | PDF

Table 1. Profile properties of output laser pulses under different uniformity coefficients

View Table | View all tables in this article

In Fig. 4, the red solid curves represent the target rectangular laser pulse profile. The simulation results of Fig. 4 demonstrate that the desired laser pulse width of 100ns is both realized by the narrow Gaussian and quasi-Gaussian input laser pulses under different uniformity coefficients. Output laser pulses by integrating Gaussian input laser pulses have better geometrical symmetry than those by integrating asymmetric quasi-Gaussian pulses. Table 1 gives shape factor, flat-top uniformity and rectangular coefficient of output laser pulses in Fig. 4. To calculate shape factor based on Eq. (10), t_top and t_bottom are respectively chosen as the pulse width of 10% and 90% maximum.

The flat-top uniformity and shape factor vary from input laser pulse shape to input laser pulse shape. Table 1 demonstrates that under the same u and M the output laser pulses integrated by Gaussian input laser pulses have larger rectangular coefficient than those integrated by quasi-Gaussian input laser pulses. For a given output laser pulse width, the input laser pulse number of M decreases with the increasing of u. In Table 1, the shape factor is improved by increasing u, and on the contrary the intensity variation of the reshaped output laser pulses is smoothed by reducing u. By synthesizing the shape factor and the flat-top uniformity, the rectangular coefficient exhibits the decline trend when increasing u.

Figure 5 shows the simulation results under different input laser pulse widths when u = 1. In Fig. 5 the desired output laser pulse width is also 100ns, and the input laser pulses still have Gaussian and quasi-Gaussian (quasi-G) shapes. Similar to Table 1, Table 2 gives the quantitative profile analysis of output laser pulses. When t_l = 100ns and M = 1, the flat-top uniformity is given as 0.5 where the valley power is defined as the power corresponding to the FWHM of t_l. Table 2 obviously demonstrates that the shape factor, flat-top uniformity and rectangular coefficient of output laser pulses can all be improved by narrowing input laser pulse width.

Fig. 5 Output laser pulse profiles under different input laser pulse widths.

Download Full Size | PDF

Table 2. Profile properties of output laser pulses under different input laser pulse widths

View Table | View all tables in this article

To sum up, the trend of the rectangular coefficient with increasing u in Table 1 demonstrates that the flat-top uniformity is more sensitive to u than the shape factor, and Table 2 shows that the shape factor is more sensitive to the non-rectangular input laser pulse width than the flat-top uniformity.

5. Establishment of trapezoidal and triangular RIPs

In this section, specific shape RIPs will be established by MPTDI, and the impacts of input laser pulses on reshaped RIPs will also be discussed in terms of the laser pulse temporal shaping model.

In 3D SRGI, the establishment of triangular and trapezoidal RIPs is necessary for the triangular and trapezoidal range-intensity correlation algorithms as illustrated in Fig. 6. The desired RIPs can be established by matching the temporal parameters of laser pulses and gate pulses. For the trapezoidal algorithm, the gate image RIPs are trapezoidal-shaped where the gate time is twice larger than the laser pulse width, and target range is r = R + I_B,head/I_A,bodyD where I_A,body and I_B,head are respectively target gray intensities in the body of gate image A and the head of gate image B, and D equals t_lc/2. For the triangular algorithm, the gate image RIPs are triangular-shaped where the gate time equals the laser pulse width, and target range is r = R + I_B,head/(I_A,tail + I_B,head)D where I_A,tail and I_B,head are respectively target gray intensities in the tail of gate image A and the head of gate image B, and D also equals t_lc/2. Here, gate image A and gate image B are two types of gate images which overlap as depicted in Fig. 6. Note that the triangular and trapezoidal RIPs mentioned in the next sections both refer to the RIPs satisfying the above algorithms.

Fig. 6 Range-intensity correlation algorithms for 3D SRGI. (a) Trapezoidal algorithm. (b) Triangular algorithm.

Download Full Size | PDF

Figure 7 shows the results of establishing trapezoidal RIPs based on the output laser pulses of Fig. 4. The gate time is 200ns, and the equivalent time delay is 200ns. In Fig. 7(a), the input laser pulses have Gaussian shape, and the RIPs under different u demonstrate that the RIP at u = 1 has a best fit with the target RIP plotted by a red solid line, when u>1 the head and tail parts have obvious intensity fluctuation, and when u<1 the linearity of the head and tail parts is better but a bias exists as illustrated in the sub windows of Fig. 7(a). The same conclusions are also obtained in Fig. 7(b) where quasi-Gaussian input laser pulses are used. Compared with Fig. 7(b), Fig. 7(a) shows better geometrical symmetry which is consistent with the results of Fig. 4. In the trapezoidal algorithm, the gray ratio is I_B,head/I_A,body. Figures 7(c) and 7(d) give gray ratio curves corresponding to Figs. 7(a) and 7(b) respectively, and obviously the Gaussian gray ratio curve at u = 1 shows the best fit with the target gray ratio curve plotted by a red solid line where a 100ns rectangular laser pulse is used.

Fig. 7 Establishment of Trapezoidal RIPs. (a) RIPs under Gaussian input laser pulses. (b) RIPs under quasi-Gaussian input laser pulses. (c) Gaussian gray ratio. (d) Quasi-Gaussian gray ratio.

Download Full Size | PDF

Figure 8 shows the results of establishing triangular RIPs where the gate time is 100ns. Gaussian and quasi-Gaussian input laser pulses in Fig. 4 are respectively used in Figs. 8(a) and 8(b). Apparently, the RIP intensity fluctuation is related to the flat-top uniformity. When u = 1 the RIPs in Figs. 8(a) and 8(b) have a best fit with the target RIP, and when u>1 the head and tail parts have obvious intensity fluctuation, and when u<1 the linearity of the head and tail parts is better but a bias also exists. Figure 8(a) shows better geometrical symmetry than Fig. 8(b). Figures 8(c) and 8(d) give gray ratio curves corresponding to Figs. 7(a) and 7(b) respectively, and obviously the Gaussian gray ratio curve at u = 1 shows the best fit with the target curve.

Fig. 8 Establishment of Triangular RIPs. (a) RIPs under Gaussian input laser pulses. (b) RIPs under quasi-Gaussian input laser pulses. (c) Gaussian gray ratio. (d) Quasi-Gaussian gray ratio.

Download Full Size | PDF

To illustrate the impact of shape factor and flat-top uniformity on the gray ratio, Fig. 9 gives the gray ratio curves at u = 1 under the trapezoidal and triangular algorithms. Note that in Figs. 7, 8 and 9, the ideal target curves denoted by “Rect” are all obtained by rectangular input laser pulses with a pulse width of 100ns, and Figs. 7(c), 7(d), 8(c), 8(d) and 9 all have the same equivalent time delay of 200ns and 300ns corresponding to gate images A and B. The results of Fig. 9 demonstrate that when the input laser pulses have symmetric Gaussian shapes, the gray ratio curves fit the target curves better, and when the input laser pulses have asymmetric quasi Gaussian shapes, the positive bias exists referring to the target curves. The reason is that the shape factor of output laser pulses integrated by Gaussian input laser pulses is 0.938 which is closer to 1 than that obtained from quasi-Gaussian input laser pulses in Table 1. In addition, compared with Gaussian gray ratio curves, the quasi-Gaussian gray ratio curves have larger fluctuation due to bad flat-top uniformity of output laser pulses in Fig. 9.

Fig. 9 Gray ratio at u = 1.(a) Gray ratio under the trapezoidal algorithm. (b) Gray ratio under the triangular algorithm.

Download Full Size | PDF

In 3D SRGI smaller gray ratio vibration results in higher range precision, and smaller bias referring to target gray ratio curves yields higher range accuracy. The gray ratio vibration and bias are determined by the flat-top uniformity and shape factor which are respectively further determined by the uniformity coefficient and input laser pulse shape and width. In fact, the gray ratio vibration corresponds to the RIP intensity fluctuation as depicted in Figs. 7 and 8. In terms of Figs. 7 and 8, to smooth the gray ratio fluctuation and improve range precision, u ≤1 is recommended. For rectangular laser pulses, the flat-top uniformity and shape factor are both 1. Table 1 shows that for Gaussian and quasi-Gaussian input laser pulses when the shape factor is closer to 1 and contrarily the flat-top uniformity is closer to 0. It seems that a tradeoff between large U and large S should be performed. Fortunately, Table 2 has proved that narrowing laser pulse width can enlarge S and also improve U. Figure 10 further proves this with an example of establishing triangular RIPs. In Fig. 10, triangular RIPs are established based on the input laser pulses of Fig. 5. When the input laser pulse width is 100ns, RIPs obtained from Gaussian and quasi-Gaussian laser pulses are not triangular-shaped. When the input laser pulse width is 1ns, RIPs obtained by the MPTDI method is consistent with the target RIP. Obviously, symmetric Gaussian input laser pulses yield symmetric RIPs, and asymmetric quasi-Gaussian input laser pulses yield asymmetric RIPs. Considering satisfying the overlap of gate images A and B as depicted in Fig. 6, symmetric RIPs are the first choice. Therefore, input laser pulses with symmetric shapes are recommended for MPTDI.

Fig. 10 Triangular RIPs under different input laser pulse widths.

Download Full Size | PDF

6. Experiments and discussions

To prove the feasibility of the proposed method, a rang-gated imaging system is established. A pulsed solid-state laser with a center wavelength of 532nm is used as illuminator, and its laser pulse width (HWFM) is 2ns at a pulse repetition frequency of 10kHz. For the gated camera, a gated GEN II intensifier is coupled to a CCD with 1024 × 1024 pixels at 15 frames per second and acts as a gate with a minimal gate time of 3ns and a maximum repetition frequency of 300kHz. The timing control unit realized by FPGA can provide desired time sequence for the pulsed laser and the gated camera.

In the experiment, the gate time is 60ns. The input laser pulse number is 30, the uniformity coefficient is 1, and thus the output laser width is 60ns. The equivalent time delay is 420ns for a type-A gate image and 480ns for a type-B gate image. Here, the type-A gate image and type-B gate image respectively refer to gate images A and gate images B mentioned in Fig. 6. Therefore, the triangular range-intensity correlation algorithm is available. The target is at about 70m. Figure 11(a) gives the gate image with the time delay of 480ns. Figures 11(b) demonstrate that the target 3D image is obtained by the MPTDI method, and the depth of 3D imaging is 9m.

Fig. 11 Experimental results of triangular 3D SRGI under MPTDI. (a) Target type-B gate image. (b) Target 3D image.

Download Full Size | PDF

For a 2ns pulsed laser, the depth of 3D imaging is fixed as 0.3m in traditional triangular 3D SRGI. Using the MPTDI method, the depth is expanded to 9m in the experiment of Fig. 11, which proves the feasibility of the MPTDI method.

5. Conclusions

By intra-frame time delay integration of multiple pulses, the gate images with flexible desired RIP shapes can be established for 3D SRGI. The proposed method of MPTDI combines the attractive features of both rectangular-shaped pulse and tunable laser pulse width for pulsed solid-sate laser illuminator. For conveniently utilizing MPTDI, a laser pulse temporal shaping model is established. Under this model, the MPTDI method is equivalent to the convolution of a gate pulse with an equivalent output laser pulse. The flat-top uniformity and shape factor of output laser pulses impact target range precision and accuracy, and they are determined by the input laser pulse shape and width as well as the uniformity coefficient. To obtain high-quality rectangular output laser pulses, input laser pulses with symmetric shape and narrow pulse width are recommended, and the uniformity coefficient is suggested no more than 1. For the MPTDI method, the advantage is that large depth of 3D imaging can be realized without scanning even using narrow pulsed solid-state lasers. The drawback is that when the depth of 3D imaging is enlarged, the range resolution is reduced. Fortunately, this drawback can be overcome by coding methods for 3D SRGI [5, 6, 15]. By embedding MPTDI in coding methods, ns-scaled rectangular laser pulses can be constructed to satisfy trapezoidal or triangular range-intensity correlation algorithms. This paper mainly gives the motivation for the MPTDI concept, and demonstrates preliminary theoretical and experimental results of MPTDI. The research is beneficial for the practical applications of 3D SRGI.

Acknowledgments

The authors acknowledge the financial funding of this work by the National Natural Science Foundation of China (NSFC) (grant 61205019) and the Hong Kong Scholars Program (grant XJ2012046).

References and links

1. M. Laurenzis, F. Christnacher, and D. Monnin, “Long-range three-dimensional active imaging with superresolution depth mapping,” Opt. Lett. 32(21), 3146–3148 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-32-21-3146. [CrossRef] [PubMed]

2. J. Busck and H. Heiselberg, “Gated viewing and high-accuracy three-dimensional laser radar,” Appl. Opt. 43(24), 4705–4710 (2004), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-43-24-4705. [CrossRef] [PubMed]

3. J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng. 44(11), 116001 (2005), http://opticalengineering.spiedigitallibrary.org/article.aspx?articleid=1101840. [CrossRef]

4. W. Xinwei, L. Youfu, and Z. Yan, “Triangular-range-intensity profile spatial-correlation method for 3D super-resolution range-gated imaging,” Appl. Opt. 52(30), 7399–7406 (2013), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-52-30-7399. [CrossRef] [PubMed]

5. M. Laurenzis and E. Bacher, “Image coding for three-dimensional range-gated imaging,” Appl. Opt. 50(21), 3824–3828 (2011), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-50-21-3824. [CrossRef] [PubMed]

6. X. Zhang and H. Yan, “Three-dimensional active imaging with maximum depth range,” Appl. Opt. 50(12), 1682–1686 (2011), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-50-12-1682. [CrossRef] [PubMed]

7. F. Christnacher, M. Laurenzis, D. Monnin, G. Schmitt, N. Metzger, S. Schertzer, and T. Scholtz, “3D laser gated viewing from a moving submarine platform,” Proc. SPIE 9250, 9250F (2014), http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1917267.

8. http://www.obzerv.com/products/.

9. I. M. Baker, S. S. Duncan, and J. W. Copley, “A low-noise laser-gated imaging system for long-range target identification,” Proc. SPIE 5406, 133–144 (2004), http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=843582. [CrossRef]

10. O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010), http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1344799. [CrossRef]

11. O. Steinvall, M. Elmqvist, T. Chevalier, and O. Gustafsson, “Active and passive short-wave infrared and near-infrared imaging for horizontal and slant paths close to ground,” Appl. Opt. 52(20), 4763–4778 (2013), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-52-20-4763. [CrossRef] [PubMed]

12. M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J.-M. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51(6), 061302 (2012), http://opticalengineering.spiedigitallibrary.org/article.aspx?articleid=1306311. [CrossRef]

13. O. Steinvall and T. Chevalier, “Range accuracy and resolution for laser radars,” Proc. SPIE 5988, 598808 (2005), http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=880859. [CrossRef]

14. P. Andersson, “Long-range three-dimensional imaging using range-gated laser radar images,” Opt. Eng. 45(3), 034301 (2006), http://opticalengineering.spiedigitallibrary.org/article.aspx?articleid=1076565. [CrossRef]

15. W. Xinwei, C. Yinan, C. Wei, L. Xiaoquan, F. Songtao, Z. Yan, and L. Youfu, “Three-dimensional range-gated flash lidar for land surface remote sensing,” Proc. SPIE 9260, 9260L (2014), http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1935278.

Input laser pulse	u	M	Output laser pulse
Input laser pulse	u	M	Shape factor	Flat-top uniformity	Rectangular coefficient
Gaussian shape	0.2	121	0.915	1	0.915
	0.5	49	0.920	1	0.920
	1	25	0.938	0.893	0.838
	2	13	0.945	0.125	0.118
	4	7	0.945	0	0
Quasi-Gaussian shape	0.2	121	0.905	0.995	0.900
	0.5	49	0.909	0.924	0.840
	1	25	0.907	0.590	0.535
	2	13	0.942	0.081	0.076
	4	7	0.943	0	0

Input laser pulse	t_l (ns)	M	Output laser pulse
Input laser pulse	t_l (ns)	M	Shape factor	Flat-top uniformity	Rectangular coefficient
Gaussian shape	100	1	0.215	0.5	0.108
	20	5	0.727	0.8923	0.648
	1	100	0.965	0.8946	0.864
Quasi-Gaussian Shape	100	1	0.202	0.5	0.101
	20	5	0.585	0.526	0.308
	1	100	0.976	0.596	0.582

Input laser pulse	u	M	Output laser pulse
Input laser pulse	u	M	Shape factor	Flat-top uniformity	Rectangular coefficient
Gaussian shape	0.2	121	0.915	1	0.915
	0.5	49	0.920	1	0.920
	1	25	0.938	0.893	0.838
	2	13	0.945	0.125	0.118
	4	7	0.945	0	0
Quasi-Gaussian shape	0.2	121	0.905	0.995	0.900
	0.5	49	0.909	0.924	0.840
	1	25	0.907	0.590	0.535
	2	13	0.942	0.081	0.076
	4	7	0.943	0	0

Input laser pulse	t_l (ns)	M	Output laser pulse
Input laser pulse	t_l (ns)	M	Shape factor	Flat-top uniformity	Rectangular coefficient
Gaussian shape	100	1	0.215	0.5	0.108
	20	5	0.727	0.8923	0.648
	1	100	0.965	0.8946	0.864
Quasi-Gaussian Shape	100	1	0.202	0.5	0.101
	20	5	0.585	0.526	0.308
	1	100	0.976	0.596	0.582

Multi-pulse time delay integration method for flexible 3D super-resolution range-gated imaging

Abstract

1. Introduction

2. Multi-pulse time delay integration method

3. Laser pulse temporal shaping model for MPTDI

4. Uniformity and rectangular characteristics of output laser pulses

5. Establishment of trapezoidal and triangular RIPs

6. Experiments and discussions

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (11)

Tables (2)

Equations (12)

Optics Express