Abstract

Flat Fresnel lenses are known to form a point image in the focal plane. However, several practical applications require transforming lens to concentrate a parallel light beam into a uniformly illuminated light circle. We previously proposed a novel algorithm for simulating such a transforming Fresnel concentrator. In this study, we applied this method to the diamond-cutting technique to create prismatic refractive surfaces of high optical quality. To reduce the discreteness of formed images, each refractive lens zone was fabricated from several small identical microprisms in the simulation. The new fabricated circular light beam concentrators were investigated by computer modelling and experimentally with a collimated laser beam.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Flat Fresnel lenses are currently utilised in many fields of applied optics [16], such as object tracking [79], precise imaging systems [1012], and concentrators for solar light in photovoltaic modules [1315]. Focusing Fresnel structures have mainly been manufactured using photolithography methods or by adjustable direct laser recording with photoresists. These methods allow the formation of known stepped structures [1,4,6] with optical defects. In practice, high-quality images are not obtained with such devices due to low optical quality of their working refractive surfaces.

The other method for Fresnel optics creation is the diamond-cutting technique [16,17], which enables the manufacturing prismatic surfaces with high optical quality and minimum mechanical defects. Accordingly, the images obtained by the lenses are also of very high quality. However, the refractive angles for the sequential microprisms in these focusing lenses can only be changed discretely, and thus only discrete images can be formed. The degree of discreteness is determined by the width of circular focusing zones; hence, the maximum size of such prismatic zones must be limited.

Focusing Fresnel lenses are usually created to form a point image in a focal plane. However, for some light signal processing systems, one must transform a parallel circular light beam into a uniformly illuminated light circle. Fresnel lenses that can achieve this transformation are often used in optical sensor systems for imaging and optoelectronic integration. They can be effectively used in concentrator modules with photovoltaic cells for solar energetics, as well as for the automatic adjustment of output signals from four-quadrant photo-detectors in different monitoring systems. We propose a method for simulating the transforming microrelief structures with flat conical refractive facets in these Fresnel lenses, which create a uniformly illuminated light circle in the focal plane.

2. Theoretical model of focusing microrelief structures

An algorithm has been proposed [18] for simulating the parameters of focusing Fresnel microprismatic structures whereby elements can be easily fabricated using a diamond-cutting technique. Here, we use this algorithm to calculate the parameters of a light concentrator, which forms the light circle at the lens focus.

As the basis for lens simulation, we used a variant of the focusing structure with a constant microrelief pitch W0. This structure allows the tool inclination angles αG and relief depth hk to be set easily, making it well-suited to the practical manufacture of such concentrators through diamond-cutting. The scheme of this structure is depicted in Fig. 1(a), where f is the focal distance; n0 and n1 are the refractive indices of the medium and the material of the microprism, respectively; Rk is the radius of lens annular zones k = 1, 2, 3,…, N; αk is the refraction angle of microprisms; γk is the observation angle for the k–zone from the central point of focus F; hk is the microrelief depth; and W is the nominal microrelief pitch. Figure 1(b) shows a real focusing lens with diameter DL = 70 mm and focal distance f = 56 mm (open aperture kL = f / DL = 0.75), made by diamond-cutting [18] according to our simulation results.

 figure: Fig. 1.

Fig. 1. (a) Scheme of circular conical Fresnel focusing element with constant relief pitch W. (b) Real microprismatic focusing lens for f / DL = 0.75.

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The angles of incidence of the rays on prismatic facets φ1k are equal to the corresponding refraction angles of prisms αk, and the angles of refraction φ2k for each conical lens k‒zone can be determined similarly to optical parameters for ophthalmology microprisms [19]. The purpose of our calculations was to obtain the angles of inclination of the flat facets of the microprisms αk = φ1k, at which the parallel beams of transmitted light are focused onto a single light point in focal plane F.

The algorithm for calculating a focusing structure suitable for the implementation of the diamond-cutting method involves, first, setting the central lens zone, which remains flat in the process of lens manufacturing. The size R1 of this zone is determined primarily by technological requirements: during diamond-cutting [17], the speed of rotation of the cutting tool at point R1 = 0 is zero; hence the value of R1 cannot be very small. On the other hand, for the formation of high-quality visual images, radius R1 cannot be too large because this increases the discreteness of formed images. Usually, a typical focusing structure has a flat zone in the centre with radius R1 = 1.0–1.2 mm to yield precise images.

A parallel light beam passes through this flat zone of radius R1 without refraction, and thus a flat area with radius r1 = R1 is formed at the centre of the focal plane. All other annular refractive lens zones with inclined flat surfaces of radii Rk and widths ΔRk should focus the transmitted light onto this single central circle of radius r1 on the focal plane of the lens.

After setting the radius of this central zone R1 at point R = R1, the angle γ1 of ray inclination for the first prismatic zone is determined. This value γ1 determines the refraction angle α1 of the circular zone k = 1 according to Snell's law [20]:

$$\begin{aligned} {{\mathrm{\gamma }_1}} &= \textrm{arctg}\;({{R_1}\; {f^{ - 1}}} )\\ {{\mathrm{\alpha }_{1}}} &= \textrm{arctg}\; \{ \textrm{sin}{\mathrm{\gamma }_1}/({{n_1}/{n_0} - \textrm{cos}{\mathrm{\gamma }_1}} )\} ) \end{aligned}$$

For refraction angle α1, the ray from point R = R1 is directed to the centre of the image formed by the lens in the focal plane F. According to the proposed calculation model, the angle α1 determines the inclination angle γ1 for all rays passing through the first annular microprism zone of width ΔR1 = (R2 - R1). The central R1 and first inclined zone R2 are formed with the same width ΔR1 = (R2 - R1) = R1, which ensures that the passed beams are focused into a single light circle of radius r1 ≈ ΔR1 = R1 (Fig. 1(a)).

After determining the radius R2 at point R = R2, the angle γ2 of ray inclination of the second prismatic zone k = 2 is determined, after which the relief parameters for zones k= 3, 4,…, N are calculated. At each simulation stage, the preliminary data are used as initial data for calculations in the following stage. Angle γk is determined for each of the conical annular zones at their point of minimum radius. It is assumed that all rays that pass through each of these conical zones with constant width ΔRk = (Rk+1 - Rk) = R1 are refracted at this same angle γk and form a circle with radius rk at the centre of the focal light spot. This radius rk diminishes with increasing Rk due to the increase of the relief depth hk = ΔRk tgαk (see Fig. 1(a)); however, the diminishing radius rk is not very important for a focusing Fresnel structure with small radius R1.

This algorithm is referred to as the model of constant relief pitch W [18]. The width ΔRk is the nominal relief pitch W0; however, this definition is more convenient for the linear refractive microprismatic structures [21] used in ophthalmology. For the annular focusing structures, we determine the parameters of the lens zones through the values of ΔRk.

For a constant relief pitch W0, the prismatic zones k = 1, 2, 3,…, N are formed with the same values of ΔRk=W0. For a constant depth of relief h0, the prismatic zones k = 1, 2, 3,…, N should be formed with the smaller values of ΔRk=h0 / tgαk for the concentration of refracted rays at the centre of focal plane F.

3. Simulation of lens concentrators

The algorithm [18] detailed in Section 2 for creating a focusing Fresnel lens allows us to obtain the radii of the circular zones Rk and the angles of refraction αk of the prismatic facets for any value of r1, f, W, the required number of relief pitches N, and required lens diameter DL. This model of constant relief pitch W was successfully employed for manufacturing focusing microprismatic Fresnel lenses using diamond-cutting (see Fig. 1(b)).

Our method [18] was upgraded [22] for simulating a microprismatic lens-concentrator. The main difference is that now it is necessary to form a uniformly illuminated light circle of a significantly larger radius r1 > 5–10 mm instead of forming the point image of a light source.

Let us consider the proposed simulation procedure in more detail for a transforming lens with a diameter DL of 52 mm, which forms a circle with radius r1 = 4.5 mm at a focal distance f of 20 mm; in this case, the open aperture kL = f / DL is approximately 0.38, which is rare. This new transforming lens will be fabricated from polycarbonate (PC) for the green-wave spectrum with a wavelength λ = 0.532 μm. Thus, the fabricated lens can be experimentally investigated with the evaluable ‘green’ laser of the same wavelength. The refractive index n1 = 1.585 for this wavelength was taken from [23]; the thickness of the forming plate was 6.0 mm. Our results show that for creating the above lens, it is necessary to form 6 prismatic zones with width ΔRk 4.5 mm. To create such a lens, several issues need to be addressed; we consider these issues in greater detail in the following subsections.

3.1 Size of central zone

When creating a microprismatic lens‒concentrator, the maximum size of the central flat zone R1 of the lens is limited by the cutting tools currently available for use in the diamond-cutting technique, such tool have a cutting edge usually no more than 1.2‒1.5 mm. Therefore, the length of inclined working surfaces of the microprisms ΔRk / cos αk or the widths of each prismatic zone ΔRk cannot be larger than ∼ 1.5 mm. To overcome this limitation, we propose the formation of each prismatic zone k = 1, 2, 3,…, N from several identical annular constituent microprismatic elements NC with the same refractive angles αk and the same widths ΔRkc. The total width ΔRk of the prismatic elements for each of these zones must be equal to the width of the central flat zone R1. The value of ΔRk = ΣΔRkc for each k–zone is defined by an appropriate variation of relief depth hk and the number of constituent elements NC. Figure 2 illustrates the simulated profile of the lens microrelief with 6 zones of identical microprisms.

 figure: Fig. 2.

Fig. 2. Simulated profile of Fresnel annular focusing structure with variable pitch ΔRk and depth hk of microrelief

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The proposed scheme is a lens model with a constant relief pitch W = R1 and structural zones with several separate identical microprisms NC of a smaller size ΔRkc. This algorithm was proposed in our previous paper [22] and allows the simulation of light beam concentrators, which form light spots of large enough size in the lens focus.

3.2 Narrowing of light beams

With an increase in the radius Rk for a constant value of ΔRk, the lens forms narrowing annular light fluxes; therefore, to completely fill the central zone of radius r1 by refracted rays in the lens focus, it is necessary to proportionally increase the values of ΔRk.

The modified scheme of the annular Fresnel focusing structure with variable relief pitch ΔRk and depth hk is shown in Fig. 2, where f is the focal length; n0 and n1 are the refractive indices of the medium and the material of the microprism, respectively; Rk is the radius of the annular zones k = 1, 2, 3,…, N; ΔRk is the width of the refractive k–zone of the lens; r1 = R1 is the radius of the light spot in focus; r0 is the radius of “dark” light zone in the centre of the image and will be discussed below; γk is the angle of observation of zone k from the central point of focus F; αk is the prism refractive angle for k‒zones; W is the nominal relief pitch; and hk is the nominal relief depth for each prismatic k‒zone.

The refracted ray for each prismatic k‒zone passes through a microprism at the point of its maximum radius Rk (point “A”, not “B” in Fig. 3), so for stated widths ΔRk= R1 with increasing refractive angle αk, the depth of relief hk increases, and the refracted ring light beams narrow accordingly due to the relief shielding. As a result, the refracted beams illuminate only the central part of the annular spot in the focal plane with different outer radii rk < r1. Thus, each prismatic k‒zone forms a narrower circle of radii rk in the focal plane. This process is clear from Fig. 3. To expand the refracted annular light flux from radius rk to radius r1, it is necessary to proportionally increase the width of the refractive zones of the lens ΔRk=R1+ ΔR'k and, accordingly, the depth of the microrelief hk=R1 tgαk+ Δh'k.

 figure: Fig. 3.

Fig. 3. Modified scheme of Fresnel annular focusing structure with variable pitch ΔRk and depth hk of microrelief

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The algorithm proposed in our earlier paper [18] accurately simulates the focusing structures only for large open apertures kL = f / DL > 1.5–2.0, when the refraction angles of microprisms αk are rather small. For larger angles αk it is necessary to change the widths of zones ΔRk and the depth of relief hk to eliminate this problem of narrowing light fluxes.

For any angle αk and γk, the values of width ΔR'k and the depth Δh'k correction can be defined as:

$$\begin{aligned} {\varDelta R{^{\prime}_{k\; }}} &= {R_1}\textrm{tg}{\alpha _k}\; \textrm{tg}{\mathrm{\gamma }_k}/({1 - \textrm{tg}{\alpha_{k\; }}\textrm{tg}{\mathrm{\gamma }_k}} )\\ {\varDelta h{^{\prime}_{k}}} &= \mathrm{\varDelta }R{^{\prime}_k}\textrm{tg}{\mathrm{\alpha }_k} \end{aligned}$$

Accordingly, the variable pitch ΔRk and depth hk of the microrelief are:

$$\begin{aligned} {\varDelta {R_{k\; }}} &= {R_1}\; \{{1 + [{\textrm{tg}{\mathrm{\alpha }_k}\; \textrm{tg}{\mathrm{\gamma }_k}/({1 - \textrm{tg}{\mathrm{\alpha }_{k\; }}\textrm{tg}{\mathrm{\gamma }_k}} )} ]} \}\\ {{h_{k}}} &= {R_1}\; \textrm{tg}{\mathrm{\alpha }_k}\{{1 + \textrm{tg}{\mathrm{\alpha }_k}\; \textrm{tg}{\gamma_k}/({1 - \textrm{tg}{\mathrm{\alpha }_{k\; }}\textrm{tg}{\mathrm{\gamma }_k}} )} \} \end{aligned}$$

Some of the results obtained are shown in Fig. 4. The simulation was performed for a lens made from PC for λ = 0.532 μm. The refractive index n1 = 1.585 was taken from [23]. It is shown that for a stated radius R1 at small refractive angles αk < 25–30 °, the correction of the width of the zone ΔR'k and corresponding depth Δh'k does not exceed 15–20%. For larger angles αk, pitch Rk and depth hk should be increased, even to unrealistic values. Therefore, it is necessary to reduce nominal relief pitch W’, which determines the value of the microrelief correction.

 figure: Fig. 4.

Fig. 4. Relative correction of pitch ΔR'k /R1 (a) and relief depth Δh'k /h'k (b) of the relief depending on the refractive angle αk for the PC lens‒concentrator for λ = 0.532 μm

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Thus, to form a uniformly illuminated light spot in the focal plane of a lens‒concentrator with a sufficiently large size compared to the size of lens prismatic zones, it is necessary to increase not only the depth of relief hk=h1+ Δh'k, but also the width of refractive zones ΔRk=R1+ ΔR'k, and to reduce the nominal relief pitch W'=R'1 (Fig. 3). Such microprismatic structure can provide illumination of the entire area of the circular zone of required diameter d1 =2r1 in the lens focus.

3.3 Radial concentration of transmitted light beams

For the considered lens, there is a noticeable concentration of light in a narrow central area of radius r0 ≈ 1.5 mm within the focal spot of radius r1 ≈ 4.5 mm. This concentration is explained by the transformation of the larger annular light fluxes when the light rings are focused with a smaller diameter. The process of light beam concentration is considered in detail in our previous paper [24], which takes into account the structure of annular focusing devices. It is well known that any traditional lens or Fresnel lens concentrates the incident circular light beam of density J0 on the centre of the formed image; the radial intensity distribution on the focal spot JCR(r) ∼ J0*(R/r), where R is the radius of the lens and r is the distance to the centre of the light spot on the focal plane. The coefficient of light concentration kCR(r) = R / r can be obtained for every circular lens zone R. Thus, to create the transforming Fresnel lens, the problem of light concentration should be resolved first.

To eliminate the central intensity maximum in the focal light circle, we propose to create the microscopic concentrator in such a way that refracted light beams at the focal plane do not fall into the area of this central maximum with radius r0 (see Fig. 3). The diameter of this central “dark” area of d0 = 2 r0 must be equal to the width of the zone with the maximum light intensity. The widths of the structural refractive lens zones ΔRk with the same refraction angle αk must also be reduced to Δr1 = r1 - r0. The angles αk for the prismatic zones must be changed accordingly.

It is assumed that this central “dark” area of the light spot in the focal plane will be illuminated by diffracted transmitted light, as well as by diffuse scattering of light, which is reflected from the lens forming plate and is chaotically refracted at the mechanical defects of the real microrelief of a fabricated lens.

Some results obtained in our paper [24] for a similar lens-concentrator for λ = 1.064 μm (n1 = 1.564 [23]) are shown in Fig. 5. The light distribution coefficient kCR(r) for an illuminated focal spot of radius r1 = 4.5 mm with contributions from different zones k = 1, 2, 3,…, N with the same width ΔRk = 4.5 mm is shown in Fig. 5(a) for zone maximum radii Rk = 9.0 mm (curve 1), 13.5 mm (2), 18.0 mm (3), 22.5 mm (4), and 27.0 mm (curve 5).

 figure: Fig. 5.

Fig. 5. Contribution of structural lens zones #1–5 (a) and #1–7 (b) as a function of lens radius Rk and total intensity distribution (c) in the focal light spot of r1 = 4.5 mm

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Figure 5(b) illustrates the same coefficient kCR(r), but for the same focal light spot of radius r1 = 4.5 mm without the central “dark” area of r0 = 1.5 mm. For this case, the width of structure zones, accordingly, is ΔRk = 3.0 mm, and the zone radii are Rk= 7.5 mm (curve 1), 10.5 mm (2), 13.5 mm (3), 16.5 mm (4), 19.5 mm (5), 22.5 mm (6), and 25.5 mm (curve 7).

Figure 5(c) shows the total light distribution JCR(r) for the central focal spot of r1 = 4.5 mm with a contribution from all the structure zones # 1–N.

As shown in the figure, the radial illumination distribution in the focal spot JCR(r) with the central “dark” area of radius r0 (curve 2) exhibits a flatter distribution (lower by approximately eight times for the considered lens) compared with the distribution for the lens without such a central area (curve 1).

3.4 Spatial homogenisation of light intensities

To diminish the light concentration effect, it is necessary to simulate the lens parameters such that each k‒zone of the lens forms a circular light spot at the focus, with the stated outer radius r1, but without the “dark” central area of radius r0. However, even in this case, the obtained light distribution at the focal spot is not completely uniform (see Fig. 5(с), curve 2). To make the light distribution in the focal annular area of Δr1 = r1 - r0 more homogeneous, we also propose the creation of structural lens zones k = 1, 2, 3,…, N such that each subsequent k‒zone forms a circular light spot at the focus with the same outer radius r1, but with the increased inner radii of the “dark” area r0k > r0.

A novel transforming lens of diameter DL= 52 mm was simulated according to this modified scheme for the “green” wavelength λ = 0.532 μm. Each of the calculated microprismatic zones # 1–6, which are necessary for the formation of this lens-concentrator, focus the transmitted light beam into an annular light spot with widths Δrk = (r1 - r0k), where r1= 4.5 mm and the radii of “dark” areas r0k= 1.5, 1.5, 2.0, 2.5, 3.0 and 3.5 mm. Thus, lens zone # 1 forms a light ring of Δr1 = 4.5 - 1.5 = 3.0 mm at the focus; zone # 2—Δr2 = 3.0 mm; zone # 3—Δr3 = 2.5 mm; zone # 4—Δr4 = 2.0 mm; zone # 5—Δr5 = 1.5 mm; and zone # 6 forms a light ring with a width of Δr6 = 1.0 mm. In our simulation, the basic relief pitch W’ has been varied from 3.0 to 1.0 mm for zones # 1–6; this allows the necessary correction of the pitch ΔR'k and depth Δh'k of the relief according to expressions (2–3).

Our simulation shows that these structure zones # 1–6 must have: four identical prismatic elements (zones # 1–2); six elements (zones # 3–5); and seven microprismatic elements (zone # 6) with the same refraction angle αk= 13.975 °, 24.769 °, 31.505 °, 35.321 °, 37.406 °, and 38.509 °. The relief depth was changed from 190 to 470 μm to obtain the required ring width Δrk = (r1 - r0k) = 3.0–1.0 mm. Such a focusing scheme provides a flatter intensity distribution JCR(r), even in the focus spot periphery.

Combining radii Rk and r0k with angles αk, it is possible to make the focal intensity distribution JCR(r) practically flat. The optimised simulated light spot distribution JCR(r) for this lens‒concentrator is shown in Fig. 6(a). The final focusing scheme is the following: the lens zones # 1‒4 focus the parallel light beam onto the focal ring of width Δrk = (r1 - r0k) = (4.5-1.5) mm (curve 1‒4), zone # 5 ‒ Δr5 = (r1 - r05) = (4.5-2.5) mm (curve 5), and prism zone # 6 ‒ Δr6 = (r1 -r06) = (4.5-3.5) mm (curve 6). Curve 7, similar to curve 2 in Fig. 5(c), represents the total effect of light beam focusing JCR(r) by all zones # 1‒6 to the single light ring of width Δrk = (r1 - r0k) = (4.5-1.5) mm.

 figure: Fig. 6.

Fig. 6. (a) Contribution of lens zones #1–6 (curves 1-6) and total effect (curve 7) as a function of lens radius Rk to focal spot of r1 = 4.5 mm without “dark” area of r0 = 1.5 mm; (b) actual manufactured “green” lens‒concentrator

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Figure 6(b) shows an actual lens‒concentrator manufactured by diamond-cutting according to the last focusing scheme; it forms a practically flat intensity distribution JCR(r) in the focal plane. Figure 2 shows just this simulated microrelief profile of the lens of diameter DL= 52 mm for the “green” wavelength λ = 0.532 μm. The scales in X and Y axis in Fig. 2 are ∼25 times different to show the peculiarity of the relief profile. For more proportional scale, similar to Fig. 3, the relief profile for separate microprismatic elements of the width ΔRk ∼ 100 µm will be practically invisible.

Our simulation shows that the creation of any focusing optics, whether traditional or microrelief, with a large light diameter DL and a small focal length f (i.e., with a small open aperture kL ≈ 0.4–0.5), leads to an appropriate decrease in the light transmission coefficient to τtr ≈ 0.5–0.6 [25] due to the increase in the reflected light coefficient τref. This must be taken into account when creating focusing devices with small values of kL = f / DL.

Thus, the results obtained show that focusing structures without the central focusing area are the most viable for the creation of a transforming microprism lens‒concentrator. An optimisation of the locations of the prismatic zones of the lens and the selection of a corresponding scheme for focusing the refracted rays allows you to achieve an almost homogeneous illumination of the spot in the lens focal plane.

4. Light beams modelling for lens concentrators

To study the optical parameters of the simulated lens‒concentrator, the programme Solidworks 2016 was used [26], which aided in the creation of the computer model of the lens. We used the simulation data for the lens-concentrator of PC for λ = 1.064 μm (n1 = 1.564). This lens model was then loaded into the programme TracePro 7.3 [27] for further modelling of the light beam paths using the geometric optics approximation and the Monte Carlo method. The light source consists of a parallel beam of rays that is evenly distributed in the plane of the lens. The screen is a disc with radius rE = 25 mm, located at the modulated test distance f from the lens.

The modulated scheme of ray propagation through the lens‒concentrator for different observation distances f = 15, 20, 25, and 50 mm is shown in Fig. 7. Light rays are shown by red, green, and blue, which indicates the light intensity of a ray in comparison to the initial intensity, corresponding to 66‒100%, 33‒66% and 01‒33% of the initial light intensity, respectively.

 figure: Fig. 7.

Fig. 7. (a) Lens‒concentrator model created using simulation data and (b) modulated scheme of parallel rays propagating through a concentrator for observation distances f = 15, 20, 25 and 50 mm

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The results obtained for point-focusing lens from PC, created for control systems with four-quadrant photo-detectors without the optimization of light refraction for infrared spectrum of λ = 1.064 μm and f = 20 mm, are shown in Fig. 8. The created lens effectively transforms the parallel light beam into the light circle in the focal plane. The main feature is the evident intensity maximum with a diameter d0 ≈ 3.0 mm in the centre of created light circle.

 figure: Fig. 8.

Fig. 8. Modulated image on screen and beam profile for PC lens for λ = 1.064 μm and f = 20 mm

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The simulation results confirm that a lens‒concentrator with a discrete change of refraction angle, in contrast to aspherical Fresnel lenses with a smooth change of refraction angle, is effective only for the calculated observation distance; at other distances, it loses its focusing properties. When altering focus distance f, the microprismatic concentrator forms a series of circular light structures, similar to those shown in Fig. 9.

 figure: Fig. 9.

Fig. 9. Modulated image on screen and beam profile for PC lens for λ = 1.064 μm and f = 50 mm

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In this transforming lens, each annular ring structure in the focal plane has the same width Δrk ≈ 4.5 mm and is formed by the constituent lens zones # 1–5. For the point of focus f = 20 mm, all these light rings are concentrated into a single light spot of radius r1 ≈ 4.5 mm, similar to that shown in Fig. 8. This light concentration is explained by the convergence of transmitted light from the wide peripheral annular zones to a narrower centre light spot.

The intensity focal distribution, which is obtained by TracePro 7.3 modelling [27] for a modified “green” lens of PC for visible spectrum of λ = 0.532 μm (n1 = 1.585), created for solar light concentration with necessary optimization of beam refraction at the lens focus, is shown in Fig. 10. The beam profile for the central area is practically flat, which corresponds to the technical specification for this lens. The small maximum in the centre (in total intensity of ∼5%) is explained by the light reflection from the inner surface of the forming PC plate and subsequent light beam concentration in the central area of focal spot.

 figure: Fig. 10.

Fig. 10. Model image at screen and beam profile for PC lens for λ = 0.532 μm and f = 20 mm

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The light profile for a forming plate of thickness δ = 6.0 mm shows an intensity that is lower than that for δ = 2.0 mm by a factor of 1.5, but showed a similar distribution, which is explained by the peculiarities of light transmission inside the model lens.

5. Experimental investigations of fabricated lens concentrators

Here, we describe the experimental setup for investigating the optical parameters of the lenses fabricated according to our simulated data. The light beam emitted by the “green” laser with wavelength λ = 0.532 μm was projected on the screen by a system of two focusing lenses: one with a power of +65 dioptres and another with a power of –20 dioptres. A condenser lens with f = 70 mm and a special diaphragm were placed in this transformed laser beam to form a nearly parallel and uniform light beam with diameter DS = 60 mm at the screen.

The tested light lens‒concentrator was placed on the optical axis of this parallel beam for different focal lengths f = 7–130 mm. In the focal plane, a moveable photodetector with a slit diaphragm of 0.4 mm width was provided, which can register the light intensity profiles at the screen. Figure 11 illustrates the general view of our experimental setup (a) and a tested lens with a typical real light distribution picture registered on the screen (b).

 figure: Fig. 11.

Fig. 11. (a) Experimental setup and (b) real picture registered at screen through lens

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Figure 12 illustrates the results of our experimental investigation of a new lens‒concentrator fabricated with six microprismatic structure zones, created for a focal distance f = 20 mm and wavelength λ = 0.532 μm. The PC lens has a diameter of DL= 52 mm and the tested distance f has been varied from 05 to 130 mm.

 figure: Fig. 12.

Fig. 12. Registered light beam distribution at screen for created “green” lens‒concentrator for focal distances f = 05–130 mm.

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An outer light ring with a diameter of DS = 60 mm corresponds to the incident light flux that passes outside the tested lens‒concentrator. These light rings are shown for every focal distances as a reference curve for easier comparison of obtained results.

For the stated focal distance f = 20 mm, the created lens forms a practically flat central light circle of radius r1 = 4.5 mm. For f < 20 mm, before the point of light beam convergence at f = 20 mm, as expected, we observe the extended light circles. For f > 25 mm, after the point of beam convergence at f = 20 mm, we see that the extended light circles are formed by divergent light beams. For f > 50 mm, we see separated light circles, each having a variable width of Δrk ≈ 1.0–3.0 mm, where radius rk increases with the focal distance f.

Our experimental data confirm that the lens with a discrete change of refraction angles is effective only for a stated observation distance; at other focal distances, the lens loses its focusing properties. The final light distributions registered for our novel “green” lens for λ = 0.532 μm for focal distances f = 5–130 mm, shown in Fig. 12, clearly illustrate the high efficiency of the lens while varying the focal distance.

Therefore, the focusing scheme of a lens‒concentrator with variable widths of light rings in the lens focus provides a uniform intensity distribution at the focal light spot. The developed concentrator samples provide the necessary transformation of the transmitted light beam into uniformly illuminated circle, which is consistent with the simulation results.

6. Conclusions

We proposed a method for the simulation of microrelief structures, which allows the development of light beam lens‒concentrators with specific refractive microrelief. The created transforming structures with discrete changes in the refraction angles provide a homogeneous intensity distribution of light intensity in the focal plane of the concentrator.

We proposed to construct the focusing structures from the groups of constituents similar microprismatic elements; such structures are suitable for fabrication by a method of diamond-cutting, which allows the formation of flat conical refractive surfaces of high optical quality.

A modified procedure for calculating the parameters of concentrators was suggested to take into account the problem of light concentration by lenses, the narrowing of light rays by microprisms and the optimization for light beam refraction.

Geometrical parameters for the relief of the annular light concentrator were calculated. Some samples of transforming circular microprismatic devices, fabricated according to the simulation results, were investigated experimentally. These manufactured lenses showed a uniformly illuminated circle in the focus of the lens, which agrees with the theoretical predictions.

The created transforming microprismatic structures are utilised now in the practical optical devices for light signal processing that allowed a reduction of the size and weight parameters of their moving parts as well as an improvement of the device performance.

The most important application of proposed plane-focusing Fresnel lenses is their using for concentration modules for solar energetics, which allow increase the efficiency of terrestrial solar panels from traditional 15–16% to 25–30% [28]. Utilization of our transforming Fresnel lenses instead of traditional point-focusing lenses allows diminish the lateral currents and, accordingly, the Ohm losses, in widespread photovoltaic cascade solar cells based on A3B5 nanoheterostructures, similar to InGaP/(In)GaAs/Ge, increasing for 3–4% the efficiency of solar energy transformation.

Funding

Science and Technology Program of Zhejiang Province (2020C01083); Natural Science Foundation of Zhejiang Province (LGG20F030009); 133 Talent Project of Yiwu City; 151 Talent Project in the Fuyang District of Hangzhou City.

Acknowledgments

The authors wish to thank the "133 Talent Project of Yiwu City" and the "151 Talent Project in the Fuyang District of Hangzhou City" for their financial support.

Disclosures

The authors declare no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

References

1. A.G. Poleshchuk, R.K. Nasyrov, and J.M. Asfour, “Combined computer-generated hologram for testing steep aspheric surfaces,” Opt. Express 17(7), 5420–5425 (2009). [CrossRef]  

2. C. A. Palmer, “Diffraction Grating Handbook (7th edition),” Newport Corporation, New York, 2014.

3. G.A. Lenkova, “High-efficiency diffractive focusing deflecting element,” Optoelectron. Instrument. Proc 51(6), 560–567 (2015). [CrossRef]  

4. V.P. Korolkov and A.G. Poleshchuk, “Laser technologies in diffractive optics,” Proc. SPIE 3733, 417–427 (1999). [CrossRef]  

5. E. Sokolova, “Simulation of mechanically ruled concave diffraction gratings by use of an original geometric theory,” Appl. Opt. 43(1), 20–28 (2004). [CrossRef]  

6. V.P. Korolkov, R.K. Nasyrov, and R.V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. 45(1), 53–62 (2006). [CrossRef]  

7. X. Liu, X. Cai, S. Chang, and C.P. Grover, “Bifocal optical system for distant object tracking,” Opt. Express 13(1), 136–141 (2005). [CrossRef]  

8. H. Huang and H. Hua, “Design of an Optical See-through Multi-Focal-Plane Stereoscopic 3D Display with Eye-tracking Ability,"OSA Technical Digest (Online), [CrossRef]  .

9. F. Wang, E. Liu, J. Yang, S. Yu, and Y. Zhou, “Target tracking in infrared imagery using a novel particle filter,” Chin. Opt. Lett. 7(7), 576–579 (2009). [CrossRef]  

10. J. Jiang, D. Zhang, S. Walker, C. Gu, Y. Ke, W.H. Yung, and S.C. Chen, “Fast 3D temporal focusing microscopy using an electrically tunable lens,” Opt. Express 23(19), 24362–24368 (2015). [CrossRef]  

11. A. Manaf, T. Sugiyama, and J. Yan, “Design and fabrication of Si-HDPE hybrid Fresnel lenses for infrared imaging systems,” Opt. Express 25(2), 1202–1220 (2017). [CrossRef]  

12. Q. Zhou, X. Li, M. Geng, H. Hu, K. Ni, L. Zhong, P. Yan, and X. Wang, “Economic fabrication of a novel hybrid planar grating/Fresnel lens for miniature spectrometers,” Opt. Express 26(5), 6079–6089 (2018). [CrossRef]  

13. T. Hornung and P. Nitz, “Light diffraction by concentrator Fresnel lenses,” Opt. Express 22(S3), A686–A704 (2014). [CrossRef]  

14. G. Vallerotto, M. Victoria, S. Askins, R. Herrero, C. Domínguez, I. Antón, and G. Sala, “Design and modeling of a cost-effective achromatic Fresnel lens for concentrating photovoltaics,” Opt. Express 24(18), A1245–A1256 (2016). [CrossRef]  

15. X. Ma, R. Jin, S. Liang, and H. Zheng, “Ideal shape of Fresnel lens for visible solar light concentration,” Opt. Express 28(12), 18141–18149 (2020). [CrossRef]  

16. E. Brinksmeier, R. GlaBe, and L. SchoNemann, “Diamond micro chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012). [CrossRef]  

17. E.E. Antonov, A.A. Kryuchyn, M.L. Fu, V.V. Petrov, and S.M. Shanoilo, “Microprisms: Optical Parameters and Monitoring,” Akademperiodyka, Kiev 146 p. (2015).

18. V.V. Petrov, E.E. Antonov, A.A. Kryuchyn, and S.M. Shanoilo, “Microprisms in ophthalmology,” Naukova Dumka, Kiev 224 p., (2019).

19. V. Petrov, A. Kryuchyn, E. Antonov, A. Lapchuk, and S. Shanoylo, “Optical phenomena in microprism diagnostic Set KK-42,” Proc. SPIE , 8011, 80119A (2011). [CrossRef]  General Congress on Optics “ICO-22”, 15-19 August (2011).

20. M. Born and E. Wolf, “Principle of optics,” Oyobuturi 7, 29 (1999). [CrossRef]  

21. E.E. Antonov, “Resolution and prismatic strength of Fresnel microprismic elements,” Data Recording, Storage&Processing 15(2), 7–16 (2013).

22. V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).

23. Refractive index database, https://refractiveindex.info/?tdsourcetag=s_pcqq_aiomsg.

24. M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021). [CrossRef]  

25. V.V. Petrov, E.E. Antonov, and S.M. Shanoilo, “Light Chromatism, diffraction and visual acuity for Fresnel microprisms,” Data Recording, Storage &Processing 12(1), 49–54 (2010).

26. SOLIDWORKS 2020, http://www.solidworks.com.

27. Software for design and analysis of illumination and optical systems, https://www.lambdares.com/tracepro.

28. V.D. Rumyantsev, “Solar concentrator modules with silicone-on-glass Fresnel lens panels and multijunction cells,” Opt. Express 18(S1), A17–A24 (2010). [CrossRef]  

References

  • View by:

  1. A.G. Poleshchuk, R.K. Nasyrov, and J.M. Asfour, “Combined computer-generated hologram for testing steep aspheric surfaces,” Opt. Express 17(7), 5420–5425 (2009).
    [Crossref]
  2. C. A. Palmer, “Diffraction Grating Handbook (7th edition),” Newport Corporation, New York, 2014.
  3. G.A. Lenkova, “High-efficiency diffractive focusing deflecting element,” Optoelectron. Instrument. Proc 51(6), 560–567 (2015).
    [Crossref]
  4. V.P. Korolkov and A.G. Poleshchuk, “Laser technologies in diffractive optics,” Proc. SPIE 3733, 417–427 (1999).
    [Crossref]
  5. E. Sokolova, “Simulation of mechanically ruled concave diffraction gratings by use of an original geometric theory,” Appl. Opt. 43(1), 20–28 (2004).
    [Crossref]
  6. V.P. Korolkov, R.K. Nasyrov, and R.V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. 45(1), 53–62 (2006).
    [Crossref]
  7. X. Liu, X. Cai, S. Chang, and C.P. Grover, “Bifocal optical system for distant object tracking,” Opt. Express 13(1), 136–141 (2005).
    [Crossref]
  8. H. Huang and H. Hua, “Design of an Optical See-through Multi-Focal-Plane Stereoscopic 3D Display with Eye-tracking Ability,"OSA Technical Digest (Online),.
    [Crossref]
  9. F. Wang, E. Liu, J. Yang, S. Yu, and Y. Zhou, “Target tracking in infrared imagery using a novel particle filter,” Chin. Opt. Lett. 7(7), 576–579 (2009).
    [Crossref]
  10. J. Jiang, D. Zhang, S. Walker, C. Gu, Y. Ke, W.H. Yung, and S.C. Chen, “Fast 3D temporal focusing microscopy using an electrically tunable lens,” Opt. Express 23(19), 24362–24368 (2015).
    [Crossref]
  11. A. Manaf, T. Sugiyama, and J. Yan, “Design and fabrication of Si-HDPE hybrid Fresnel lenses for infrared imaging systems,” Opt. Express 25(2), 1202–1220 (2017).
    [Crossref]
  12. Q. Zhou, X. Li, M. Geng, H. Hu, K. Ni, L. Zhong, P. Yan, and X. Wang, “Economic fabrication of a novel hybrid planar grating/Fresnel lens for miniature spectrometers,” Opt. Express 26(5), 6079–6089 (2018).
    [Crossref]
  13. T. Hornung and P. Nitz, “Light diffraction by concentrator Fresnel lenses,” Opt. Express 22(S3), A686–A704 (2014).
    [Crossref]
  14. G. Vallerotto, M. Victoria, S. Askins, R. Herrero, C. Domínguez, I. Antón, and G. Sala, “Design and modeling of a cost-effective achromatic Fresnel lens for concentrating photovoltaics,” Opt. Express 24(18), A1245–A1256 (2016).
    [Crossref]
  15. X. Ma, R. Jin, S. Liang, and H. Zheng, “Ideal shape of Fresnel lens for visible solar light concentration,” Opt. Express 28(12), 18141–18149 (2020).
    [Crossref]
  16. E. Brinksmeier, R. GlaBe, and L. SchoNemann, “Diamond micro chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
    [Crossref]
  17. E.E. Antonov, A.A. Kryuchyn, M.L. Fu, V.V. Petrov, and S.M. Shanoilo, “Microprisms: Optical Parameters and Monitoring,” Akademperiodyka, Kiev 146 p. (2015).
  18. V.V. Petrov, E.E. Antonov, A.A. Kryuchyn, and S.M. Shanoilo, “Microprisms in ophthalmology,” Naukova Dumka, Kiev 224 p., (2019).
  19. V. Petrov, A. Kryuchyn, E. Antonov, A. Lapchuk, and S. Shanoylo, “Optical phenomena in microprism diagnostic Set KK-42,” Proc. SPIE, 8011, 80119A (2011). General Congress on Optics “ICO-22”, 15-19 August (2011).
    [Crossref]
  20. M. Born and E. Wolf, “Principle of optics,” Oyobuturi 7, 29 (1999).
    [Crossref]
  21. E.E. Antonov, “Resolution and prismatic strength of Fresnel microprismic elements,” Data Recording, Storage&Processing 15(2), 7–16 (2013).
  22. V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).
  23. Refractive index database, https://refractiveindex.info/?tdsourcetag=s_pcqq_aiomsg .
  24. M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021).
    [Crossref]
  25. V.V. Petrov, E.E. Antonov, and S.M. Shanoilo, “Light Chromatism, diffraction and visual acuity for Fresnel microprisms,” Data Recording, Storage &Processing 12(1), 49–54 (2010).
  26. SOLIDWORKS 2020, http://www.solidworks.com .
  27. Software for design and analysis of illumination and optical systems, https://www.lambdares.com/tracepro .
  28. V.D. Rumyantsev, “Solar concentrator modules with silicone-on-glass Fresnel lens panels and multijunction cells,” Opt. Express 18(S1), A17–A24 (2010).
    [Crossref]

2021 (1)

M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021).
[Crossref]

2020 (2)

V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).

X. Ma, R. Jin, S. Liang, and H. Zheng, “Ideal shape of Fresnel lens for visible solar light concentration,” Opt. Express 28(12), 18141–18149 (2020).
[Crossref]

2018 (1)

2017 (1)

2016 (1)

2015 (2)

2014 (1)

2013 (1)

E.E. Antonov, “Resolution and prismatic strength of Fresnel microprismic elements,” Data Recording, Storage&Processing 15(2), 7–16 (2013).

2012 (1)

E. Brinksmeier, R. GlaBe, and L. SchoNemann, “Diamond micro chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]

2011 (1)

V. Petrov, A. Kryuchyn, E. Antonov, A. Lapchuk, and S. Shanoylo, “Optical phenomena in microprism diagnostic Set KK-42,” Proc. SPIE, 8011, 80119A (2011). General Congress on Optics “ICO-22”, 15-19 August (2011).
[Crossref]

2010 (2)

V.V. Petrov, E.E. Antonov, and S.M. Shanoilo, “Light Chromatism, diffraction and visual acuity for Fresnel microprisms,” Data Recording, Storage &Processing 12(1), 49–54 (2010).

V.D. Rumyantsev, “Solar concentrator modules with silicone-on-glass Fresnel lens panels and multijunction cells,” Opt. Express 18(S1), A17–A24 (2010).
[Crossref]

2009 (2)

2006 (1)

2005 (1)

2004 (1)

1999 (2)

V.P. Korolkov and A.G. Poleshchuk, “Laser technologies in diffractive optics,” Proc. SPIE 3733, 417–427 (1999).
[Crossref]

M. Born and E. Wolf, “Principle of optics,” Oyobuturi 7, 29 (1999).
[Crossref]

Antón, I.

Antonov, E.

V. Petrov, A. Kryuchyn, E. Antonov, A. Lapchuk, and S. Shanoylo, “Optical phenomena in microprism diagnostic Set KK-42,” Proc. SPIE, 8011, 80119A (2011). General Congress on Optics “ICO-22”, 15-19 August (2011).
[Crossref]

Antonov, E.E.

M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021).
[Crossref]

V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).

E.E. Antonov, “Resolution and prismatic strength of Fresnel microprismic elements,” Data Recording, Storage&Processing 15(2), 7–16 (2013).

V.V. Petrov, E.E. Antonov, and S.M. Shanoilo, “Light Chromatism, diffraction and visual acuity for Fresnel microprisms,” Data Recording, Storage &Processing 12(1), 49–54 (2010).

E.E. Antonov, A.A. Kryuchyn, M.L. Fu, V.V. Petrov, and S.M. Shanoilo, “Microprisms: Optical Parameters and Monitoring,” Akademperiodyka, Kiev 146 p. (2015).

V.V. Petrov, E.E. Antonov, A.A. Kryuchyn, and S.M. Shanoilo, “Microprisms in ophthalmology,” Naukova Dumka, Kiev 224 p., (2019).

Asfour, J.M.

Askins, S.

Born, M.

M. Born and E. Wolf, “Principle of optics,” Oyobuturi 7, 29 (1999).
[Crossref]

Brinksmeier, E.

E. Brinksmeier, R. GlaBe, and L. SchoNemann, “Diamond micro chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]

Cai, X.

Chang, S.

Chen, S.C.

Domínguez, C.

Fu, M.L.

M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021).
[Crossref]

E.E. Antonov, A.A. Kryuchyn, M.L. Fu, V.V. Petrov, and S.M. Shanoilo, “Microprisms: Optical Parameters and Monitoring,” Akademperiodyka, Kiev 146 p. (2015).

Geng, M.

GlaBe, R.

E. Brinksmeier, R. GlaBe, and L. SchoNemann, “Diamond micro chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]

Grover, C.P.

Gu, C.

Herrero, R.

Hornung, T.

Hu, H.

Hua, H.

H. Huang and H. Hua, “Design of an Optical See-through Multi-Focal-Plane Stereoscopic 3D Display with Eye-tracking Ability,"OSA Technical Digest (Online),.
[Crossref]

Huang, H.

H. Huang and H. Hua, “Design of an Optical See-through Multi-Focal-Plane Stereoscopic 3D Display with Eye-tracking Ability,"OSA Technical Digest (Online),.
[Crossref]

Jiang, J.

Jin, R.

Ke, Y.

Korolkov, V.P.

Kryuchyn, A.

V. Petrov, A. Kryuchyn, E. Antonov, A. Lapchuk, and S. Shanoylo, “Optical phenomena in microprism diagnostic Set KK-42,” Proc. SPIE, 8011, 80119A (2011). General Congress on Optics “ICO-22”, 15-19 August (2011).
[Crossref]

Kryuchyn, A.A.

E.E. Antonov, A.A. Kryuchyn, M.L. Fu, V.V. Petrov, and S.M. Shanoilo, “Microprisms: Optical Parameters and Monitoring,” Akademperiodyka, Kiev 146 p. (2015).

V.V. Petrov, E.E. Antonov, A.A. Kryuchyn, and S.M. Shanoilo, “Microprisms in ophthalmology,” Naukova Dumka, Kiev 224 p., (2019).

Lapchuk, A.

V. Petrov, A. Kryuchyn, E. Antonov, A. Lapchuk, and S. Shanoylo, “Optical phenomena in microprism diagnostic Set KK-42,” Proc. SPIE, 8011, 80119A (2011). General Congress on Optics “ICO-22”, 15-19 August (2011).
[Crossref]

Lenkova, G.A.

G.A. Lenkova, “High-efficiency diffractive focusing deflecting element,” Optoelectron. Instrument. Proc 51(6), 560–567 (2015).
[Crossref]

Li, X.

Liang, S.

Liu, E.

Liu, X.

Ma, X.

Manaf, A.

Manko, D. Yu.

M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021).
[Crossref]

Manko, D.Y.

V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).

Nasyrov, R.K.

Ni, K.

Nitz, P.

Palmer, C. A.

C. A. Palmer, “Diffraction Grating Handbook (7th edition),” Newport Corporation, New York, 2014.

Petrov, V.

V. Petrov, A. Kryuchyn, E. Antonov, A. Lapchuk, and S. Shanoylo, “Optical phenomena in microprism diagnostic Set KK-42,” Proc. SPIE, 8011, 80119A (2011). General Congress on Optics “ICO-22”, 15-19 August (2011).
[Crossref]

Petrov, V.V.

M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021).
[Crossref]

V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).

V.V. Petrov, E.E. Antonov, and S.M. Shanoilo, “Light Chromatism, diffraction and visual acuity for Fresnel microprisms,” Data Recording, Storage &Processing 12(1), 49–54 (2010).

V.V. Petrov, E.E. Antonov, A.A. Kryuchyn, and S.M. Shanoilo, “Microprisms in ophthalmology,” Naukova Dumka, Kiev 224 p., (2019).

E.E. Antonov, A.A. Kryuchyn, M.L. Fu, V.V. Petrov, and S.M. Shanoilo, “Microprisms: Optical Parameters and Monitoring,” Akademperiodyka, Kiev 146 p. (2015).

Poleshchuk, A.G.

Rong, K.Z.

M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021).
[Crossref]

Rumyantsev, V.D.

Sala, G.

SchoNemann, L.

E. Brinksmeier, R. GlaBe, and L. SchoNemann, “Diamond micro chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]

Shanoilo, S.M.

V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).

V.V. Petrov, E.E. Antonov, and S.M. Shanoilo, “Light Chromatism, diffraction and visual acuity for Fresnel microprisms,” Data Recording, Storage &Processing 12(1), 49–54 (2010).

E.E. Antonov, A.A. Kryuchyn, M.L. Fu, V.V. Petrov, and S.M. Shanoilo, “Microprisms: Optical Parameters and Monitoring,” Akademperiodyka, Kiev 146 p. (2015).

V.V. Petrov, E.E. Antonov, A.A. Kryuchyn, and S.M. Shanoilo, “Microprisms in ophthalmology,” Naukova Dumka, Kiev 224 p., (2019).

Shanoylo, S.

V. Petrov, A. Kryuchyn, E. Antonov, A. Lapchuk, and S. Shanoylo, “Optical phenomena in microprism diagnostic Set KK-42,” Proc. SPIE, 8011, 80119A (2011). General Congress on Optics “ICO-22”, 15-19 August (2011).
[Crossref]

Shimansky, R.V.

Sokolova, E.

Sugiyama, T.

Vallerotto, G.

Victoria, M.

Walker, S.

Wang, F.

Wang, X.

Wolf, E.

M. Born and E. Wolf, “Principle of optics,” Oyobuturi 7, 29 (1999).
[Crossref]

Yan, J.

Yan, P.

Yang, J.

Yu, S.

Yung, W.H.

Zenin, V.N.

V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).

Zhang, D.

Zheng, H.

Zhong, L.

Zhou, Q.

Zhou, Y.

Appl. Opt. (2)

Chin. Opt. Lett. (1)

Data Recording, Storage &Processing (1)

V.V. Petrov, E.E. Antonov, and S.M. Shanoilo, “Light Chromatism, diffraction and visual acuity for Fresnel microprisms,” Data Recording, Storage &Processing 12(1), 49–54 (2010).

Data Recording, Storage&Processing (2)

E.E. Antonov, “Resolution and prismatic strength of Fresnel microprismic elements,” Data Recording, Storage&Processing 15(2), 7–16 (2013).

V.V. Petrov, E.E. Antonov, D.Y. Manko, V.N. Zenin, and S.M. Shanoilo, “Simulation and investigation of parameters for light beam concentrators,” Data Recording, Storage&Processing 22(3), 3–13 (2020).

IEEE Photonics J. (1)

M.L. Fu, E.E. Antonov, D. Yu. Manko, V.V. Petrov, and K.Z. Rong, “Microprismatic Fresnel Lens for Formation of Uniform Light Circle,” IEEE Photonics J. 13(3), 2200108 (2021).
[Crossref]

Opt. Express (9)

V.D. Rumyantsev, “Solar concentrator modules with silicone-on-glass Fresnel lens panels and multijunction cells,” Opt. Express 18(S1), A17–A24 (2010).
[Crossref]

J. Jiang, D. Zhang, S. Walker, C. Gu, Y. Ke, W.H. Yung, and S.C. Chen, “Fast 3D temporal focusing microscopy using an electrically tunable lens,” Opt. Express 23(19), 24362–24368 (2015).
[Crossref]

A. Manaf, T. Sugiyama, and J. Yan, “Design and fabrication of Si-HDPE hybrid Fresnel lenses for infrared imaging systems,” Opt. Express 25(2), 1202–1220 (2017).
[Crossref]

Q. Zhou, X. Li, M. Geng, H. Hu, K. Ni, L. Zhong, P. Yan, and X. Wang, “Economic fabrication of a novel hybrid planar grating/Fresnel lens for miniature spectrometers,” Opt. Express 26(5), 6079–6089 (2018).
[Crossref]

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Data availability

No data were generated or analyzed in the presented research.

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Figures (12)

Fig. 1.
Fig. 1. (a) Scheme of circular conical Fresnel focusing element with constant relief pitch W. (b) Real microprismatic focusing lens for f / DL = 0.75.
Fig. 2.
Fig. 2. Simulated profile of Fresnel annular focusing structure with variable pitch ΔRk and depth hk of microrelief
Fig. 3.
Fig. 3. Modified scheme of Fresnel annular focusing structure with variable pitch ΔRk and depth hk of microrelief
Fig. 4.
Fig. 4. Relative correction of pitch ΔR'k /R1 (a) and relief depth Δh'k /h'k (b) of the relief depending on the refractive angle αk for the PC lens‒concentrator for λ = 0.532 μm
Fig. 5.
Fig. 5. Contribution of structural lens zones #1–5 (a) and #1–7 (b) as a function of lens radius Rk and total intensity distribution (c) in the focal light spot of r1 = 4.5 mm
Fig. 6.
Fig. 6. (a) Contribution of lens zones #1–6 (curves 1-6) and total effect (curve 7) as a function of lens radius Rk to focal spot of r1 = 4.5 mm without “dark” area of r0 = 1.5 mm; (b) actual manufactured “green” lens‒concentrator
Fig. 7.
Fig. 7. (a) Lens‒concentrator model created using simulation data and (b) modulated scheme of parallel rays propagating through a concentrator for observation distances f = 15, 20, 25 and 50 mm
Fig. 8.
Fig. 8. Modulated image on screen and beam profile for PC lens for λ = 1.064 μm and f = 20 mm
Fig. 9.
Fig. 9. Modulated image on screen and beam profile for PC lens for λ = 1.064 μm and f = 50 mm
Fig. 10.
Fig. 10. Model image at screen and beam profile for PC lens for λ = 0.532 μm and f = 20 mm
Fig. 11.
Fig. 11. (a) Experimental setup and (b) real picture registered at screen through lens
Fig. 12.
Fig. 12. Registered light beam distribution at screen for created “green” lens‒concentrator for focal distances f = 05–130 mm.

Equations (3)

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γ 1 = arctg ( R 1 f 1 ) α 1 = arctg { sin γ 1 / ( n 1 / n 0 cos γ 1 ) } )
Δ R k = R 1 tg α k tg γ k / ( 1 tg α k tg γ k ) Δ h k = Δ R k tg α k
Δ R k = R 1 { 1 + [ tg α k tg γ k / ( 1 tg α k tg γ k ) ] } h k = R 1 tg α k { 1 + tg α k tg γ k / ( 1 tg α k tg γ k ) }

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