作者简介:艾月霞(1980—),女,深圳大学助理研究员. 研究方向:瞬态光电技术. E-mail:email@example.com
中文责编:晨 兮; 英文责编:木 南
Shenzhen Key Laboratory of Micro-Nano Photonic Information Technology, College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, Guangdong Province, P.R.China
To get more precise high-speed streak cameras, we analyze a novel optical-deflection accelerating technique for light-beam. When the incident light-beam is deflected with a tiny initial deflection angle, according to the law of curved surface reflection, the reflective light-beam is deflected therewith and the deflection angle is enlarged. The deflecting amplification accelerating device can amplify the small deflecting angle by one to two orders of magnitude through adjust the curvature of the curved-surface. This device dominates the optical information capacity in tubeless streak camera, such as rotating mirror cameras, electro-optic crystal deflector cameras, and other light-beam scanning devices. Because there is no mechanical moving part in the new-developed device, this technique is suitable for cooperating with electro-optical deflection and the Goos-Hänchen displacement.
In the field of microsecond imaging, the interest is back to high speed rotating mirror cameras. To date, in fact, there has been no electronic camera yet that can match a rotating mirror camera with film, which possesses a bigger frame format of 102 mm2 order, more frame count than a hundred frames, higher spatial resolution, larger dynamic range of 103 or more, and so on. Lai et al[1-2] have done the innovative and valuable researches on it. This kind of camera is predominantly used in the field of shock waves and detonation physics[3-5]. In the Shardin formula, optical information capacity which is the product of imaging frequency ν, spatial resolution N and the size of frame B in the time direction depends on the rotating mirror edge line-speed νp and the wavelength of light λ. Having considered the optical accelerating, the Shardin's formula is perfected by
where β, the most important parameter in the optical accelerating circle, is an optical accelerating factor of 2～200 usually.
The multi-reflection accelerating can multiply the deflection speed of the incident light-beam on the reflective surface of rotational mirror and can be divided into two schemes[6-9]: multi-reflection with wadge-gap-shaped retroreflector and multi-reflection with rotating polyhedron mirror. According to the law of reflection, the factor β for this kind of optical accelerating can be expressed by
where n is the number of reflection on rotational reflecting surfaces of the wadge-gap-shaped retroreflector or the rotating polyhedron mirror. And the angular velocity Ω of the outgoing beam after reflecting can be written as Ω=2nω, where ω is the angular velocity of the retroreflector or the rotating polyhedron mirror.
The multi-reflection with wadge-gap-shaped retroreflector has especially promoted the rotating mirror streak camera with temporal resolution of nanosecond. As is shown in Fig.1, the deflection mode of galvanometer with the wedge-gap-shaped retroreflector is the combination of a rotational mirror and a stationary mirror, or two rotational mirrors with opposite directions. The streak camera prototype, based on this retroreflector, is an important breakthrough in the rotating mirror imaging field, and has a lot of excellent performances such as higher sensitivity, broader linear dynamic region, finer spatial contrast(a spatial resolution of 10 lp/mm), high temporal resolution(11.4 ns at 3.8 ns/pixel), larger information capacity and better adaptability, compared with the electronic camera, side-by-side testing.
The version of the galvanometer mentioned above, the wadge-gap-shaped retroreflector formed by a pair of rotating mirrors of two cones with opposite direction, is one of classical cameras and available in operation.
In this scheme, the number of reflection n, directly dominating the angular velocity of the outgoing beam which determines the optical information capacity for the framing imaging or the temporal resolution for streak imaging, is 16 for the double rotational mirrors with opposite direction and additional stationary folding mirror. The number of reflection n which is dependent upon the incident angle ψ of the imaging beam, the inclination δ between two deflecting mirrors, and the reflectivity of the mirrors, can be written by
Another multi-reflection with rotating polyhedron mirror has several models of combination of polyhedron mirrors with static mirrors to give birth to different accelerating factors. For example, as shown in Fig.2, the accelerator is composed of a rotating nine-sided mirror polyhedron 1, a collimating lens 2 and a triple prism 3, which is a typical arrangement with the optical accelerating factor β of 4 which means that as the polyhedron rotates by an angle of θ, the light beam rotates by an angle of 4θ.
Both the multi-reflection with wadge-gap-shaped retroreflector and the multi-reflection with rotating polyhedron mirror, practically applied to the rotating mirror cameras, should meet two conditions. One condition is to be provided with a very exact rotating device, and the other one is to make the relative locations between the multiple reflecting light-beam and the reflective mirrors accurate. Therefore, the multi-reflection accelerating should be performed by accurately calculating and designing, and its device is complicated in structure and high in cost.
The deflection amplification accelerating, different from that mentioned above and carried out by a curved surface mirror, is a new optical accelerating technique in which the small deflecting angle is to be amplified, continuously.
The key point of the accelerating is to mainly make the incident light-beam with tiny deflecting angles or tiny displacements sequentially be projected on different locations of a spatially curved surface to form different incident angles during the deflecting period. Based upon the law of reflection, the reflective angle and its incident angle are equal and continuously changing. The change range of the reflective angles is limited by the incident light-beam locations on the curved surface and the curvature of the curved surface which can both be designed according to requirements. Therefore, both scanning of the incident light-beam and amplifying deflection angles can be performed. The optical accelerating factor β is related to structural parameters, such as the relative location of the system configured for generating the original tiny deflections and displacements, and the curvatures of the curved surface.
As a rule, in this situation, the optical accelerating equation can be expressed by
where, as shown in Fig.3, φ is an original tiny deflection angle, γ is formed by the outgoing beam with the incident beam, Ω is the accelerated angular velocity and ω is the original angular velocity generated by an electro-optical deflector. Here, the optical accelerating factor β is around 2 to 200 usually. The optical information capacity of this kind of imaging technique which is now with advantage in the nanosecond and sub-nanosecond imaging field, can be increased by 1 to 2 orders of magnitude.
As shown in Fig.3, r is a radius of the cylindrical reflector and its curvature is ρ=1/r. Its normal crosses x-axis at point C. An incident angle at an incident point T is θ, thus its deflection angle relative to an incident optical axis is γ=2θ+φ, and θ=φ+α. Now the optical accelerating factor β can be deduced as follows
β=dγ/dφ=2((L+r)/r)(cos φ)/(cos θ)-1(5)
As shown, β is not a constant from Eq.(5)for this reflective mirror. When the original deflection angle φ is tiny,α and θ are small enough, β can be approximately written by
where L is a distance between an original deflection point and a vertex of the cylindrical-surface reflective mirror. As it is seen from Eq.(6), the optical accelerating factor is determined by ρ and L, and β is a constant in this supposed condition.
Now we can further study the optical accelerating factor β. As it is shown, β is not a constant from Eq.(5)for the cylindrical reflector. In general, if the reflective curved mirror is some transcendental curved cylindrical-surface, described by the following differential Eq.(7), the optical accelerating factor could be a constant:
where the initial condition is(L,0). And as tan-1(y/x)～y/x, then Eq.(7)can be deduced to
The analytic solution of Eq.(8)is
As shown in Fig.4, the blue curve for the analytic solution of Eq.(9)is in very good agreement the black curve for the numeric solution of Eq.(7)near y=0 when β=50.
Fig.4 The analytic solution of Eq.(9)and the numeric solution of Eq.(7)(x-axis normalized by length L)
According to Eq.(6), the optical accelerating factor β can be increased more if ρ increases. However, when ρ increases, the radius of the curved-surface reflective mirror will be decreased. Thus the curced-surface mirror is difficult to process and apply. Generally speaking, the light-beam deflection angle or the deflection speed can be improved by one to two orders of magnitude. In addition, no mechanical moving device is found in this accelerating device, such as the rotating polyhedron mirror and the retroreflector. Thus it is simple and more suitable for cooperating with the electro-optical deflection and the Goos-Hänchen displacement[12-13] to accelerate the light-beam deflection.
It is found that the deflection amplification accelerating can be used to improve the temporal resolution of the crystal-streak camera 20.0 ps to 2.5 ps at least.
Two kinds of accelerating principle, mentioned above, are very useful and available in the ultra high speed rotating mirror cameras, framing and streak, and electro-optical deflecting recording devices. Both the multi-reflection accelerating and the deflecting amplification accelerating can effectively accelerate the deflecting speed of the incident light-beam for greatly increasing the optical information capacity. However, the former is complicated in structure and high in cost. The latter, different from the former, is a newly invented optical deflecting technique, in which the small deflecting angle can be amplified by one to two orders of magnitude. Its device, moreover, may have not any mechanical rotating parts, so it is simple and more suitable for cooperating with the electro-optical deflection and the Goos-Hänchen displacement to accelerate the light-beam deflection.As having simultaneously considered both the multi-reflection accelerating and the deflecting amplification accelerating, the optical accelerating factor β should be expressed by
On the understanding that n=16, dγ/dφ=16, which are reasonable and reliable, the factor β=512, which suggests an attractive prospect.
At last, the optica deflection accelerating techniques, upgrading the optical information capacity, can be applied to the ultra-high speed rotating polyhedron mirror devices and other scanning devices. Especially, the optical-deflection amplification accelerating, useful and available, may have a great perspective.