A spherical aberration-free continuous-focus micro-liquid core cylindrical lens system based on PDMS substrate

Abstract

The present invention relates to a zoom optical system, in particular to a spherical aberration continuous zoom micro liquid core cylindrical lens system based on a PDMS substrate, which is composed of a capillary buried in a micro PDMS substrate and a double convex cylindrical lens. When a glycerol aqueous solution with a refractive index of 1.3330 to 1.4730 is injected into the capillary, the focal length of the optical system is f Achievable 8.928 mm ~2.675 mm The continuous and smooth change of the optical system’s diffuse spot RMS radius on the focal plane is always less than 5.0 in the entire zoom range. μm ; When the focal length is 8.928 mm ~3.118 mm In the range, the peak-to-valley wavefront aberration is less than λ / 4, and the imaging quality is close to the diffraction limit. The cylindrical lens system has the advantages of small size, convenient operation, good stability and high imaging quality.

Description

Technical Field

[0001] The invention belongs to a zoom optical system, and in particular relates to an aplanatic continuous zoom liquid core cylindrical lens system. Background Art

[0002] Solid zoom devices are gradually unable to adapt to the needs of optical devices such as miniaturization and integration of optical communications, optical imaging, and Lab-On-a-Chip. Liquid-filled variable focus lenses have the advantages of various adjustment methods and large focal length changes, and have become a research hotspot in recent years. Considering the imaging quality of the lens, in addition to the zoom range of the lens system, spherical aberration is an important factor affecting the imaging quality of liquid zoom lenses under monochromatic light. In order to achieve the purpose of eliminating spherical aberration, Mishra et al. reshaped the quasi-spherical optical interface into a non-spherical interface by applying electrostatic force, which required additional electromotive force, and its structure was complex and difficult to operate. Fuh et al. used two layers of polyvinyl chloride film of different thicknesses to compensate for spherical aberration. This method has a large adjustment range, but the spherical aberration correction effect is limited.

[0003] PDMS is polydimethylsiloxane (full name in English: polydimethylsiloxane), a transparent organic polymer material, including a main agent and a hardener, which can produce a solid transparent PDMS substrate. In order to provide a "laboratory on a chip" as an optical imaging element, in 2013, the inventor's team used PDMS as a substrate to make a variable focus micro-column lens, and published "Variable Focus Column Lens Based on PDMS Substrate" (China Optics, Vol. 6, No. 3, p368-369, March 2013). This column lens is mainly composed of a glass capillary buried in the PDMS substrate, and the zoom function is achieved by selecting the refractive index of the liquid in the capillary. When the refractive index of the liquid is 1.4518-1.5502, the focal length of the column lens can be reduced from 21.369mm to 3.362mm, and the zoom ratio reaches 6.4 times. The scattered light imaging method was used to observe and photograph the light trajectory of parallel light passing through this variable focus cylindrical lens. The figure is consistent with the results of the imaging process simulated by ZEMAX optical design software. The focal length formula of this cylindrical lens was derived using the successive imaging method of Gaussian optics. The calculation results of the focal length are consistent with the experimental and simulation results, providing an important optical imaging element for the "laboratory on a chip". However, the cylindrical lens is designed to achieve the zoom function, and the aberration is not included in the design content, which affects the imaging quality of the liquid zoom lens under monochromatic light. Summary of the invention

[0004] In order to solve the above problems, the purpose of the present invention is to provide a spherical aberration continuous zoom micro liquid core column lens system based on a PDMS substrate incorporating a compact capillary and a double convex lens structure and a liquid with a small refractive index filled in the capillary. The system can achieve a continuous and smooth change in the focal length of the lens system and has a good spherical aberration effect in the entire zoom range.

[0005] The above objectives are achieved through the following means:

[0006] (I) A spherical aberration continuous zoom micro liquid core cylindrical lens system based on PDMS substrate

[0007] The spherical aberration continuous zoom micro liquid core cylindrical lens system based on PDMS substrate includes:

[0008] A) A micro PDMS substrate;

[0009] B) a slit aperture attached to the left side of the PDMS substrate;

[0010] C) The capillary and the double convex lens are sequentially embedded in the PDMS substrate along the right side of the slit aperture, and

[0011] The rear wall of the capillary is in close contact with the front surface of the double convex lens.

[0012] The capillary is injected with glycerol aqueous solutions of different concentrations to form a liquid core; here, the concentration of the glycerol solution C 液 With the liquid core refractive index n 液 (n 液 =n4) one-to-one correspondence, n 液 It also corresponds to the focal length f of the lens system. 液 The focal length f is a composite function of the incident mapping to achieve a spherical aberration continuous zoom. The focal length f of the lens system is derived as follows:

[0013]

[0014]

[0015] s2=∞ (1c)

[0016] s i+1 =s' i -d i (i=2,3,…,7) (1d)

[0017]

[0018] u i+1 =u' i (i=2,3,…,7) (1f)

[0019] u'2=u2+i2-i2 (1g)

[0020]

[0021] In the above formula, D represents the diameter of the aperture, s i 、s' i Respectively represent the object intercept and image intercept of the i-th cylinder, u i 、u' i They represent the object-side aperture angle and image-side aperture angle of the i-th optical surface respectively, and i2 and i'2 represent the incident angle and refraction angle of the second optical surface respectively.

[0022] Further, in the micro liquid core cylindrical lens system:

[0023] The PDMS substrate is a cuboid with a size of 5.0 mm×2.0 mm×2.0 mm;

[0024] The width of the slit aperture on the left side of the PDMS substrate is 0.7 mm;

[0025] The capillary tube wall has an outer radius R of 1.00 mm, an inner radius r of 0.70 mm, a height h of 2.0 mm, is made of K9 glass, and the distance between the front wall of the capillary tube and the front wall of PDMS is 0.3 mm;

[0026] The biconvex cylindrical lens is made of F2 glass, and the curvature radii of the front and rear surfaces are R 凸1 =1.40mm, R 凸2 =-1.10mm, thickness is 1.1mm, height h is 2.0mm, the front surface of the double convex lens is in close contact with the back wall of the capillary, and the distance between the back surface and the back wall of PDMS is 1.6mm;

[0027] The amount of glycerol aqueous solution injected into the capillary was 3 μL.

[0028] Furthermore, the micro liquid core cylindrical lens system:

[0029] When the concentration of the glycerol aqueous solution is 0-1, the corresponding refractive index is 1.3330-1.4730, and the focal length f of the lens system can achieve a continuous and smooth change from 8.928 mm to 2.675 mm, with a magnification ratio greater than 3.

[0030] Furthermore, the micro liquid core cylindrical lens system:

[0031] In the entire zoom range, the root mean square radius of the diffuse spot on the focal plane of the system is ultimately less than 5 μm; when the focal length is in the range of 3.118 mm to 8.928 mm, the peak-to-valley wavefront difference is less than λ / 4, and the imaging quality is close to the diffraction limit.

[0032] (II) Zooming method and capability of cylindrical lens system of the present invention

[0033] According to the focal length f of the lens system, the recursive formula (1a~1h) is used to change the refractive index n of the liquid core in the capillary tube according to the following method. 液 (n 液 =n4), the method is:

[0034] Inject different concentrations of glycerol aqueous solution into the capillary to form a liquid core with a refractive index n 液 With glycerol solution concentration C 液 One-to-one correspondence, n 液 =g(C 液 ). According to equations (1a to 1h), the focal length f and n of the lens system 液 There is also a one-to-one correspondence between the focal length f and the concentration C 液 Therefore, by changing the concentration of the glycerol aqueous solution injected into the capillary, the focal length of the lens system with a spherical aberration can be continuously changed.

[0035] 1. Zoom capability of the aplanatic continuous zoom micro-liquid core cylindrical lens system based on PDMS substrate

[0036] The refractive index of pure water is 1.3330, and the refractive index of propylene glycol is 1.4730. propylene glycol and water can be miscible in any proportion. Therefore, the refractive index of propylene glycol aqueous solution can be continuously changed between 1.3330 and 1.4730. According to equations (1a to 1h), the focal length of the lens system can be continuously and smoothly changed between 8.928 mm and 2.675 mm. Table 1 shows the refractive index n of the lens system with different liquid cores. 液 The corresponding focal length f, Fig.10 Corresponding to Table 1, it reflects the zoom capability of the lens system.

[0037] Table 1 Correspondence between focal length of lens system and refractive index of liquid core

[0038]

[0039] 2. Imaging quality analysis of the aplanatic continuous-focus micro-liquid core cylindrical lens system based on PDMS substrate

[0040] To illustrate the imaging quality of this lens system, we used ZEMAX software to simulate and obtain the focal plane diffuse spot root mean square radius (RMS) and peak-to-valley wavefront aberration (MWA) corresponding to the lens system at different liquid core refractive indices and different focal lengths, and calculated the corresponding Airy disk radius size by the formula 1.22λ*f / D, as shown in Table 2 and Fig.11 , Fig.12 The curve is listed in Table 2. Fig.11 , Fig.12 All show that when n 液 When the focal length f of the lens system changes from 1.3330 to 1.4730 and changes continuously from 8.928mm to 2.675mm, the root mean square radius (RMS) of the diffuse spot of the imaging system on the focal plane is always less than 5.0μm in the entire zoom range; when the focal length f is in the range of 3.000mm to 8.928mm, the root mean square radius (RMS) of the diffuse spot of the imaging system on the focal plane is smaller than the corresponding Airy disk radius; when the focal length f is in the range of 3.118mm to 8.928mm, the peak-to-valley wavefront aberration (MWA) is less than λ / 4, and the imaging quality is close to the diffraction limit. Table 2 and Fig.11 , Fig.12 It shows that the imaging quality of the aplanatic continuous-focus micro-liquid core cylindrical lens system based on the PDMS substrate designed by the present invention is close to the diffraction limit within a zoom range of more than 90%.

[0041] Table 2 RMS value and MWA value of lens system focal length in the whole zoom range

[0042]

[0043]

[0044] Compared with the previous related literature, the cylindrical lens system designed by the present invention has the following positive effects due to its technical features:

[0045] 1. Only a single capillary is embedded in the PDMS substrate, without a double convex cylindrical lens and a slit aperture. However, this system embeds both of them in the PDMS substrate at the same time. The double convex cylindrical lens and the slit aperture enhance the focusing ability of the cylindrical lens system.

[0046] 2. Use a commonly used glycerol aqueous solution with high permeability, low liquid refractive index, and no toxicity. When the concentration of the glycerol aqueous solution injected into the liquid core of the cylindrical lens system increases from 0 to 1, the liquid refractive index n 液 Changing from 1.3330 to 1.4730, the cylindrical lens system can achieve a continuous and smooth change of focal length from 8.928mm to 2.657mm, with a zoom ratio greater than 3;

[0047] 3. The asphere aberration is incorporated into the design. In the entire liquid zoom range, the root mean square radius of the diffuse spot of the lens system on the focal plane is always less than 5μm. When the focal length is in the range of 3.118mm to 8.928mm, the peak-to-valley wavefront aberration is less than λ / 4, and the imaging quality is close to the diffraction limit. Not only can a better zoom function be achieved, but also a good asphere aberration effect is achieved.

[0048] 4. The liquid core consumption of this cylindrical lens system is only 3μL;

[0049] 5. The overall size is small, 5.0mm×2.0mm×2.0mm, which is easy to integrate. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The schematic diagram of the continuous zoom micro liquid core cylindrical lens system of the present invention is composed of a capillary buried in a PDMS substrate and a double convex cylindrical lens, including eight optical curved surfaces, and liquid can be injected into the capillary to form a liquid core.

[0051] Figure 2 It is a schematic diagram of the first and second refraction principles of the continuous zoom micro liquid core cylindrical lens system of the present invention.

[0052] Figure 3 It is a schematic diagram of the third refraction principle of the continuous zoom micro liquid core cylindrical lens system of the present invention.

[0053] Figure 4 It is a schematic diagram of the fourth refraction principle of the continuous zoom micro liquid core cylindrical lens system of the present invention.

[0054] Figure 5 It is a schematic diagram of the fifth refraction principle of the continuous zoom micro liquid core cylindrical lens system of the present invention.

[0055] Figure 6 It is a schematic diagram of the sixth refraction principle of the continuous zoom micro liquid core cylindrical lens system of the present invention.

[0056] Figure 7 It is a schematic diagram of the seventh refraction principle of the continuous zoom micro liquid core cylindrical lens system of the present invention.

[0057] Figure 8 It is a schematic diagram of the eighth refraction principle of the continuous zoom micro liquid core cylindrical lens system of the present invention.

[0058] Fig. 9 This is a ray tracing diagram of parallel light passing through a lens system injected with glycerol aqueous solutions of different concentrations, simulated by ZEMAX optical design software. Fig. 9 (a)-9(d) are n 液 =1.3330, 1.3500, 1.3900, 1.4730, the corresponding focal lengths are f=8.928mm, 6.817mm, 4.445mm, 2.675mm respectively.

[0059] Fig.10 The focal length f of the lens system varies with the refractive index n of the glycerol aqueous solution. 液 The change curve.

[0060] Fig.11It is the curve of the root mean square radius (RMS) of the diffuse spot on the focal plane of the lens system and the radius of the Airy disk with the focal length f of the lens system. Among them, the dotted line graph -■- represents the curve of the RMS with the focal length f of the lens system, and the solid line - represents the curve of the radius of the Airy disk with the focal length f of the lens system.

[0061] Fig.12 It is the curve of the peak-to-valley wavefront aberration (MWA) on the focal plane of the lens system with the focal length f. Among them, the dotted line graph -■- represents the curve of the MWA with the focal length, and the λ / 4 value is marked by the solid line -.

[0062] The present invention is further described in the following specific embodiments in conjunction with the accompanying drawings. The protection scope of the present invention includes the following embodiments and modifications, supplements and changes made to the embodiments with conventional technical solutions. DETAILED DESCRIPTION

[0063] (I) Physical structure and parameters of the lens system of the present invention

[0064] like Figure 1 As shown, the lens system of the present invention is composed of a capillary buried in a PDMS substrate and a double convex cylindrical lens: the capillary wall is made of K9 glass, including four cylindrical optical surfaces, and liquid can be injected into the cylindrical cavity in the middle to form a liquid core; the double convex cylindrical lens is made of F2 glass, including two cylindrical optical surfaces to weaken the spherical aberration of the lens system; the PDMS substrate is a rectangular substrate, including two front and rear planes to play a refractive role; a slit diaphragm with a width of 0.7 mm is pasted on the front wall of the PDMS substrate.

[0065] The invented lens system includes 8 optical surfaces, and its parameters are:

[0066] The curvature radii of the eight optical surfaces are R1 = R8 = ∞, R2 = -R5 = R = 1.00 mm, R3 = -R4 = r = 0.70 mm, R6 = R 凸1 =1.40mm, R7=R 凸2 =-1.10mm;

[0067] The intervals between adjacent optical curved surfaces are d1 = d2 = d4 = 0.3 mm, d3 = 1.4 mm, d5 = 0, d6 = 1.1 mm, d7 = 1.6 mm;

[0068] The PDMS substrate is placed in the air, that is, n1 = n'8 = 1; the capillary and the double convex lens are buried in the PDMS substrate, then n2(n'1) = n6(n'5) = n8(n'7) = n PDMS =1.4115; the capillary material is K9 glass, n3(n'2)=n5(n'4)=n K9=1.5168; the refractive index of the liquid core is determined by the concentration of the injected glycerol aqueous solution, n4(n'3)=n 液 ; The convex lens material is F2 glass, then n7(n'6)=n F2 =1.62004;

[0069] The PDMS substrate is a cuboid with dimensions of 5.0 mm × 2.0 mm × 2.0 mm. The half widths of the first, second, fifth, sixth, seventh, and eighth optical surfaces are h1 = 1.0 mm, and the half widths of the second and third optical surfaces are h2 = 0.7 mm. The heights of the capillary and the double convex lens are both h = 2.0 mm, and the aperture diameter is determined by the width of the slit diaphragm, which is D = 0.7 mm.

[0070] (II) Zooming capability of the lens system of the present invention with a spherical aberration

[0071] According to Gaussian optics, the recursive formula for the focal length f of the lens system can be derived:

[0072]

[0073]

[0074] s2 =∞ (1c)

[0075] s i+1 =s' i -d i (i=2,3,…,7) (1d)

[0076]

[0077] u i+1 =u' i (i=2,3,…,7) (1f)

[0078] u'2=u2+i2-i'2 (1g)

[0079]

[0080] (1a~1h) where D represents the diameter of the aperture, s i , s′ i Respectively represent the object intercept and image intercept of the i-th cylinder, u i , u′ i Represent the object side aperture angle and image side aperture angle of the i-th optical surface, respectively, i2 and i'2 represent the incident angle and refraction angle of the second optical surface, respectively. It can be seen from (1a~1h) that the concentration C of the glycerol solution 液 With the liquid core refractive index n 液 (n 液 =n4) one-to-one correspondence, n液 It also corresponds to the focal length f of the lens system. 液 The focal length f is a composite function of the incident image, which is mapped by changing the refractive index n of the liquid core in the capillary 液 The lens system can achieve continuous focal length change with a spherical aberration.

[0081] Fig. 9 This is a ray tracing diagram of parallel light passing through a lens system injected with glycerol aqueous solutions of different concentrations, simulated by ZEMAX optical design software. The refractive index of pure water is 1.3330, and the refractive index of analytical pure glycerol is 1.4730. Glycerol and water can be miscible in any proportion, so by changing the concentration of the glycerol aqueous solution, n 液 Continuous change from 1.3330 to 1.4730. Fig. 9 (a)-9(d) are n 液 =1.3330, 1.3500, 1.3900, 1.4730, the corresponding focal lengths are f=8.928mm, 6.817mm, 4.445mm, 2.675mm respectively.

[0082] Fig.10 The focal length f of the lens system varies with the refractive index n of the glycerol aqueous solution. 液 When the liquid core of the lens system is injected with liquid with a refractive index of n 液 When changing from 1.3330 to 1.4730, the f can be continuously changed from 8.928mm to 2.675mm, achieving a zoom ratio greater than 3:1, and the entire focal length change process is smooth. Fig. 9 , Fig.10 This directly reflects that the lens system of the present invention has the zoom capability of eliminating spherical aberration.

[0083] (III) Analysis of imaging quality of the lens system of the present invention

[0084] For zoom lens systems illuminated by monochromatic parallel light, spherical aberration is the main factor affecting its imaging quality. Reasonable design of the curvature radius, thickness and glass material of the optical surfaces of the slit aperture, capillary and biconvex lens can limit the spherical aberration of the lens system in the entire zoom range. Fig.11 , 12 The imaging quality of the lens system of the present invention is described in detail.

[0085] Fig.11It is the curve of the root mean square radius (RMS) of the diffuse spot on the focal plane of the lens system and the radius of the Airy disk changing with the focal length f of the lens system. Among them, the dotted line graph -■- represents the curve of the RMS changing with the focal length f of the lens system, and the solid line - represents the curve of the Airy disk radius changing with the focal length f of the lens system. The root mean square radius (RMS) of the diffuse spot on the focal plane of the lens system changing with the focal length value of the system is obtained by performing ray tracing simulation one by one using the ZEMAX optical design software, and the Airy disk radius size is calculated by the formula 1.22λ*f / D. When the root mean square radius (RMS) of the diffuse spot is smaller than the Airy disk radius, it can be considered that its imaging quality is good and close to the diffraction limit. From Fig.11 It can be seen that when the focal length of the lens system is greater than 3 mm, the root mean square radius (RMS) of the diffuse spot of the lens system on the focal plane is smaller than the radius of the Airy disk, and the root mean square radius (RMS) of the diffuse spot of the lens system on the focal plane is always less than 5 μm in the entire zoom range.

[0086] Fig.12 It is the curve of the change of the peak-to-valley wavefront aberration (MWA) on the focal plane of the lens system with the focal length f. Among them, the dotted line graph -■- represents the change of the MWA with the focal length f, and the λ / 4 value is marked by the solid line -. The peak-to-valley wavefront aberration (MWA) on the focal plane of the lens system at different focal lengths is simulated one by one by the ZEMAX optical design software. According to the Rayleigh criterion, when the peak-to-valley wavefront aberration of the optical system is less than or equal to λ / 4, there is no significant difference in the imaging quality between the system and the ideal system. Fig.12 It can be seen that when the focal length of the lens system is greater than 3.118 mm, the peak-to-valley wavefront aberration of the lens system on the focal plane is less than λ / 4.

[0087] Fig.11 , Fig.12 It is intuitively reflected that, no matter judging by the diffuse spot radius size or the Rayleigh criterion, the lens system maintains a high imaging quality within a zoom range greater than 90%, which is close to the diffraction limit.

[0088] The structure and use of the above-mentioned aplanatic continuous-focus micro-liquid core cylindrical lens system based on the PDMS substrate fall within the protection scope of the present invention.

Claims

1. A spherical aberration continuous zoom micro liquid core cylindrical lens system based on PDMS substrate, including: A) A micro PDMS substrate; B) a slit aperture attached to the left side of the PDMS substrate; C) The capillary and the double convex lens are sequentially embedded in the PDMS substrate along the right side of the slit aperture, and The rear wall of the capillary is in close contact with the front surface of the double convex lens. The capillary is injected with glycerol aqueous solutions of different concentrations to form a liquid core; here, the concentration of the glycerol solution C 液 With the liquid core refractive index n 液 =n4 one-to-one correspondence, n 液 It also corresponds to the focal length f of the lens system. 液 The focal length f is a composite function of the incident mapping to achieve a spherical aberration continuous zoom. The focal length f of the lens system is derived as follows: s2=∞ (1c) yes i+1 =s′ i -d i (i=2,3,...,7) (1d) in i+1 =u′ i (i=2,3,...,7) (1f) u'2=u2+i2-i'2 (1g) In the above formula, D represents the diameter of the aperture, s i , s′ i Respectively represent the object intercept and image intercept of the i-th cylinder, u i , u′ i Respectively represent the object-side aperture angle and image-side aperture angle of the i-th optical surface, i1 and i′1 represent the incident angle and refraction angle of the first optical surface, i2 and i2′ represent the incident angle and refraction angle of the second optical surface, n i With n i ' are the image-side refractive index and object-side refractive index of the i-th optical cylinder, and Ri is the radius of curvature of the front and back surfaces of the double convex cylindrical lens.

2. The micro-liquid core cylindrical lens system according to claim 1, characterized in that: The PDMS substrate is a cuboid with a size of 5.0 mm×2.0 mm×2.0 mm; The slit aperture width on the left side of the PDMS substrate is 0.7 mm; The capillary tube wall has an outer radius R of 1.00 mm, an inner radius r of 0.70 mm, a height h of 2.0 mm, is made of K9 glass, and the distance between the front wall of the capillary tube and the front wall of PDMS is 0.3 mm; The curvature radii of the front and rear surfaces of the double convex cylindrical lens are R 凸1 =1.40mm, R 凸2 =-1.10mm, thickness is 1.1mm, height h is 2.0mm, the front surface of the double convex lens is in close contact with the back wall of the capillary, and the distance between the back surface and the back wall of PDMS is 1.6mm; The amount of glycerol aqueous solution injected into the capillary was 3 μL.

3. The micro-liquid core cylindrical lens system according to claim 1 or 2, characterized in that: When the concentration of the glycerol aqueous solution is 0-1, the corresponding refractive index is 1.3330-1.4730, and the focal length f of the lens system can achieve a continuous and smooth change from 8.928 mm to 2.675 mm, and the magnification ratio is greater than 3.

4. The micro-liquid core cylindrical lens system according to claim 1 or 2, characterized in that In the entire zoom range, the root mean square radius of the diffuse spot on the focal plane of the system is ultimately less than 5 μm; when the focal length is in the range of 3.118 mm to 8.928 mm, the peak-to-valley wavefront difference is less than λ / 4, and the imaging quality is close to the diffraction limit.

5. The micro-liquid core cylindrical lens system according to claim 3, characterized in that In the entire zoom range, the root mean square radius of the diffuse spot on the focal plane of the system is ultimately less than 5 μm; when the focal length is in the range of 3.118 mm to 8.928 mm, the peak-to-valley wavefront difference is less than λ / 4, and the imaging quality is close to the diffraction limit.

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