MX2010005792A - Optical system with variable field depth. - Google Patents

Abstract

An optical lens which, in a controlled manner, and without altering either the resolution or luminous capture, helps to extend the depth of field of any other optical system. The optical lens of the present invention is composed of two optical lenses that form a pair. Each of the lenses of the pair produces a change of optical path with a symmetrical distribution. If there is no relative displacement, the lenses of the pair generate an optical path difference equal to zero. When there is relative displacement, the lenses of the pair generate a change of optical path with asymmetric distribution, which helps to extend the depth of field without reducing either the resolution or luminous capture. The optical lens of this invention, in the form of an optical pair, serves any other optical system to capture images without loss of modulation, but with attenuated modulation which can be retrieved with digital processing algorithms known in the art.

Description

OPTICAL SYSTEM WITH DEPTH OF VARIABLE FIELD DESCRIPTION OBJECT OF THE INVENTION A process and a device to control the depth of field of an optical system, by shifting between two lenses that make up the pair, which is capable of generating an optical path difference with antisymmetric distribution.

An optical system composed of one or several lenses already known in the art, which may include an image processing system also known in the art, and includes one or more pairs of lenses that generate an optical path difference with anti-symmetric distribution, which occurs with a relative displacement between the lenses that make up the pair. The transmittance in complex amplitude of a lens of the pair is the complex conjugate of the transmittance in complex amplitude of the other lens.

BACKGROUND It is convenient to describe an optical system that captures the image of a three-dimensional object as a process of transfer between planes. When using an optical system, only one plane of the object is well focused on the plane in which the image is detected. The other planes of the object are not well focused on the plane in which the image is detected. It is common to indicate that for the other planes of the object, the optical system suffers from focusing errors.

The tolerance with which the optical system is able to capture the other planes of the object, is known as depth of field, which is controlled by opening or closing the aperture of the pupil of the optical system. Closing the pupil gives greater depth of field. However, closing the pupil also reduces the resolution of the optical system and the light collection of said optical system, as described in Leo Levi, Applied Optics: A Guide to Optical System Design / Volume I. (Wiley, 1968) ISBN -10: 0471531103. If it is desired to preserve the resolution and the light collection of the optical system it is necessary to find a new method to control the depth of field.

In the last two decades several devices were designed to maintain high resolution and extend the depth of field, moderately and selectively attenuating some areas of the pupil. See for example the publications "Improvement in the OTF of a Defocused Optical System Through the Use of Shade Apertures," Appl. Opt. 10, 2219 (1971); J. Ojeda-Castaneda, L. Berriel-Valdos, and E. Montes, "Line spread Function relatively Insensitive to Defocus," Opt. Lett. 8,458 (1983); G. Indebetow and H. Bai, "Imaging with Fresnel Zone Pupils Masks: Extended Depth of Field," Appl. Opt. 23, 4299 (1984); J. Ojeda-Castaneda, L. Berriel-Valdos, and E. Montes, "Spatial Filter for Increasing the Depth of Focus," Opt. Lett. 10, 520 (1985); J. Ojeda-Castaneda, P. Andres, and A. Diaz, "Annular Apodizer for Low Sensitivity to Defocus and to Spherical Aberration," Opt. Lett. 11, 487 (1986). These designs lead to the conclusion that to maintain a pre-specified resolution, it is possible to form the images of several planes of the object, but the cosinoidal variations (in other planes of the object) are formed with attenuated amplitude. Consequently, there must be several lens families that (for a pre-specified resolution) extend the depth of field with images that present cosine variations with low amplitude. Since these images only require amplification in their amplitude, this is achieved by employing restoration algorithms known in the art.

From these last conclusions, to extend depth of field, the new designs have the purpose of reducing the influence of focusing errors, and thus avoid that the amplitude of the cosinoidal variations be zero. Once the images have been captured, the amplitude is restored with algorithms known in the art, as discussed in patents US6,927,922 and US7,218,448.

To find a new method of depth-of-field control, it is convenient to mathematically model the image-forming optical system as a linear system, see for example the book "Introduction to Fourier Optics" by Joseph W. Goodman (McGraw-Hill, 1996). , ISBN-10: 0070242542.

A linear system is represented by an optical transfer function. The module of the optical transfer function is the transfer function of the modulation. This last function specifies with what new amplitude is detected (in the plane of the image) the initial amplitude of a cosine variation that is located in a plane of the object. The transfer function of the modulation specifies the transfer of the amplitudes for each frequency of the cosine variation, so it is useful to represent the quality of an optical system, and hence the convenience of evaluating said function. For this, the mathematical operation of autocorrelation of the generalized function of the pupil is performed, which describes the transmittance in complex amplitude of the optical system. The generalized function of the pupil is a complex function, which results from multiplying the actual function that represents the physical opening of the pupil, by the transmittance in complex amplitude of the optical filter, which is located on the opening of the pupil. In a conventional system the transmittance in complex amplitude of the optical filter is equal to one. However, in order to improve the modulation transfer function, and consequently to improve the quality of the image, it is necessary to modify the transmittance in complex amplitude of the optical filter, as indicated in references J. Ojeda-Castaneda and LR Berriel-Valdos, "Arbitrarily high focal depth with finite apernares," Opt. Lett. 13, 183-185 (1988); "Zone píate for arbitrarily high focal depth", J. Ojeda-Castañeda and L. R. Berriel-Valdos, Applied Optics, Vol. 29, No. 7, p. 994-997 (1990).

To take into account the influence of focusing errors it is necessary to incorporate a quadratic phase factor in the coordinates of the pupil. In the latter case, it is convenient to use the mathematical formalism of the ambiguity function, associated with the complex amplitude transmittance of the optical filter. The mathematical formalism of the ambiguity function makes it possible to identify the transmittance in complex amplitude of the optical filter that is less sensitive to focusing errors, as discussed in J. Ojeda-Castañeda, LR Berriel-Valdos, and E. Montes, "Ambiguity function as a design tool for high focal depth, "Appl. Opt. 27, 790-795 (1988).

In order to reduce the impact of the focusing errors, without affecting the resolution and the light acquisition of the optical system, a transmittance in complex amplitude is sought which is a function only of the phase. A transmittance in complex amplitude that reduces the impact of the focusing error, is capable of extending the depth of field to a specific value, which is determined by the maximum optical path difference introduced by the optical filter, as indicated in patent US5,748,371 and in the publications E. R. Dowski and T. W. Cathey, "Extended depth of field through wave-front coding," Appl. Opt. 34, 1859-1865 (1995); A. Sauceda and J. Ojeda-Castaneda, "High focal depth with fractional-power wave fronts," Opt. Lett. 29, 560-562 (2004); A. Castro and J. Ojeda-Castañeda, "Asymmetric phase masks for extended depth of field," Appl. Opt. 43, 3474-3479 (2004); A. Castro, J. Ojeda-Castaneda, and A. W. Lohmann, "Bow-tie effect: differential operator," Appl. Opt. 45, 7878-7884 (2006).

Patent US5,748,371 describes a method for extending the depth of field, to a specific value using only one lens. In the present invention, a method is protected to extend the depth of field in a controlled manner, from a minimum value to a maximum value using a pair of lenses. This is possible by varying in a controlled manner the optical path difference that the proposed lens is capable of generating.

One possible way to vary the optical path difference in a controlled manner is by applying the methodology described in US Pat. No. 3,305,294, wherein a method for varying the optical power is described by means of the lateral displacement between two lenses, which have a profile that varies as a cubic polynomial.

Unlike US Pat. No. 3,305,294, a method for varying the depth of field is protected in the present invention, while in US Pat. No. 3,305,294 a method for varying the optical power is described.

In other words, a method for varying, in a controlled manner, the depth of field extension is described in the present invention, while in US Pat. No. 5,748,361 the depth of field extension is constant. In the present invention, describes a method for extending the depth of field, while in US Pat. No. 3,305,294 a method for varying the optical power is described.

BRIEF DESCRIPTION OF THE FIGURES In the figure, a side view of the lenses 1 and 2 is presented, which constitute the pair integrating the lens proposed in the present invention. Between 1 and 2 there is no relative displacement. In figure Ib it is indicated that between 1 and 2 there is relative displacement.

In Figure 2 is exposed in a lateral schematic diagram when the proposed lens (1 and 2) is located in the pupil (4) of a telecentric optical system (3 and 5) as is common in optical image processing.

In Figure 3 the use of the proposed lens (1 and 2), located in the pupil (4), of a Cooke triplet (6, 7 and 8) as commonly used in a lens, is shown in a lateral schematic diagram. photographic.

In figure 4 the use of the proposed lens (10) is shown in a block diagram in an optical pick-up system (9), a detection system (11), and a signal processing system and / or images (12).

Figure 5 shows a graph where the horizontal axis denotes the variation of the coordinate of the pupil a, and the vertical axis denotes the variation of the optical path difference f (a).

Figure 6 shows nine numerical simulations of the images captured by an optical system. By using an optical system known in the art (13), the images obtained using a system with the lens of the present invention, without using processing digital (14), and the images obtained using a system with the lens of the present invention after restoring the detected amplitude (15).

In (16) an image with focusing errors is shown which is obtained by an optical system known in the art. In (17) an image with focusing errors is shown which is obtained by an optical system with the lens of the present invention before restoration. In (18) an image with focusing errors is shown which is obtained by an optical system with the lens of the present invention after the restoration. In (19) an image with large focusing errors is shown which is obtained by an optical system known in the art. In (20) an image with large focusing errors is shown which is obtained by an optical system with the lens of the present invention before restoration. In (21) there is shown an image with large focusing errors that is obtained by an optical system with the lens of the present invention after the restoration. It can be seen from (15), (18) and (21) that the images obtained using the lens of the present invention have the quality independently of the focusing error. Therefore, the present invention is capable of extending the depth of field.

In Figure 7a the modulation transfer function that is achieved with a conventional lens known in the art, or with the lens of the present invention, is exhibited if there is no relative displacement between the lenses of the pair.

The transfer function of the modulation that is achieved with the lens of the present invention is shown in Figure 7b, with relative displacement between the lenses of the pair.

DETAILED DESCRIPTION OF THE INVENTION The present invention consists of an optical lens which in turn is formed by two lenses to form the pair. A pair lens has a complex amplitude transmittance that describes an optical path difference with symmetric distribution. The transmittance in complex amplitude of a lens of the pair is the complex conjugate of the transmittance in complex amplitude of the other lens of the pair.

In mathematical terms, it is convenient to denote the coordinate in the pupil by the letter a, and its range of variation (-O, O) is the opening of the pupil. The transmittance in complex amplitude of the first lens of the pair is denoted as ?? (a) = exp [i 2 p a f (a)] (1) In equation 1, the maximum optical path difference is a, and the function f (a) is a real function whose values are bounded between -1 and 1. It is convenient to note to make a lens with the optical path difference f ( a), that this difference depends both on the variations of the refractive index N (a), and on the variations of the lens profile f (a). In mathematical terms, f (a) = [? (a) - 1]? (a) (2) Figure 5 shows an example of a symmetric distribution for the function f (a). The transmittance in complex amplitude of the second lens of the pair is defined by ? 2 (a) = ?? * (a) = exp [- i 2 p a f (a)] (3) In equation 3 the asterisk denotes the conjugate complex. Now, if there is a displacement v between the optical lenses that constitute the pair, the following transmittance in complex amplitude is generated ? (a;?) =?, (a +? / 2)? 2 (a -? / 2) =?, (a +? / 2)?, * (a -? / 2) (4) If equation 1 is used, in equation 4 the latter can be expressed as ? (a; v) = exp. { i 2p a [f (a + v / 2) - f (a - v / 2)]} (5) In the present invention it is selected that the function f (a) is a symmetric function in the variable, with the property that the optical path difference in equation 5 is an antisymmetric distribution in variable a. That is, respectively, it must be fulfilled that f (a) = f (- a) (6) f (a +? / 2) - f (a -? / 2) = - [f (a - v / 2) - f (a + v / 2)] (7) The conditions for the optical path differences expressed in equations 6 and 7 are clarified below with two illustrative examples.

EXAMPLES Next, a novel optical path distribution f (a) exemplifying the present invention is discussed. If selected f (a) = cos (na / 2Q) (8) In equation 8 the Greek letter O denotes (as indicated before equation 1) the upper limit of a. It should be recognized in equation 8 that the function 5 5 (a / 2O) is a symmetric function in a, so it is straightforward to verify that equation 8 satisfies the condition of equation 6. Additionally, from equation 8 it is easy to obtain that the optical path difference is f (a + v / 2) - f (a -? / 2) = - [2 sin (7w / 4Q)] sin (a / 2Q) (9) Again it is straightforward to verify that the result of equation 9 satisfies the condition in equation 7.

Additionally, it is obtained from equation 9, that the sin function (7ia / 2Q) is amplified by the factor [25e? (? / 4O)]. This amplification factor only depends on the variable v, which, as is known, represents the displacement between the lenses of the pair used in the present invention. Thus for zero displacement, v = 0, the optical path difference in equation 9 is zero. However, for values of v other than zero, the multiplication factor can be increased. So through the displacement v it is possible to control the amplification factor of the sin function (n: a / 2Q). This novel illustrative example clarifies the methodology used to control the optical path difference described by the sin (na / 2Q) function.

Now, on the other hand, if the function 8e? (Pa / 2O) is used with a fixed amplification factor, then it is possible to extend the depth of field as it is public domain from the publication of A. Castro, J. Ojeda-Castañeda, and AW Lohmann, "Bow-tie effect: differential operator," Appl. Opt. 45, 7878-7884 (2006).

In this last publication it is indicated that an optical path difference of the sin form (7ia / 2Q) extends the depth of field, as can be seen in the numerical simulations shown in figure 6. In this figure it is shown throughout of the lines both the focused image and the image with focusing errors. Throughout the first column of figure 6 the images obtained with an optical system known in the art are shown. Throughout the second column of figure 6 the images obtained with the lens of the present invention without using restoration are shown, and along the third column the images obtained using the lens of the present invention and restoration algorithms known in the art are shown.

It is relevant to emphasize that the depth of field extension achieved in the publication "Bow-tie effect: differential operator," Appl. Opt. 45, 7878-7884 (2006) using only a lens with an optical path difference function of the sen (ra / 2Q) type, has the same limitation as that reported in the patent US5,748,371. In both cases the Field extension is fixed. While in the present invention, by using two lenses, the optical path difference of the sen (na / 2) type is amplified by the factor [2 sin (7tv / 4D)]. So it is possible to control the depth of field extension.

A similar result can be obtained to the one already discussed, with the use of the function in equation 1, if a lens with complex amplitude transmittance of the type is used. ?? (a) = exp [i 2p a (a / O) 4] (10) This transmittance in complex amplitude is reported in the publication of Jorge Ojeda-Castañeda, J. E. Landgrave and Cristina M. Gómez-Sarabia, "Conjúgate phase píate use in analysis of the frequency response of optical systems designed for extended depth of field". The transmittance in complex amplitude in Equation 10 is another example of the use of the methodology proposed in the present invention.

In Figure 7a the modulation transfer function that is obtained using a conventional lens, known in the art, or using the lens of the present invention without relative displacement between the lenses that compose the pair is exhibited. The targeting error is plotted on the x axis. On the y-axis the frequency of the cosine variation is plotted. On the z-axis, we graph how well the amplitudes are transferred in the cosine variations. It can be seen that as the focusing error increases, the Transfer of the amplitudes is damped and zeros appear in the transfer process. What results in loss of information.

Figure 7b shows the modulation transfer function that is obtained using the lens of the present invention with relative displacement between the lenses that make up the pair. The targeting error is plotted on the x axis. On the y-axis the frequency of the cosine variation is plotted. On the z-axis, we graph how well the amplitudes are transferred in the cosine variations. It can be seen that the changes of the z axis are smooth with respect to the variation in the x axis. So the transfer of the amplitudes is relatively insensitive to focusing errors. Which means that no information is lost.

The lens of the present invention can be used to reduce the length of zoom lenses, to optimize photolithography processes, to extend the depth of field in robotic vision, in microscopy, for terrestrial telescopes, for photographic lenses, and in acquisition systems of images for cell phones and personal computers.

Claims (4)

CLAIMS Having described enough my invention "OPTICAL SYSTEM WITH DEPTH OF VARIABLE FIELD" I claim as my property contained in the following claims:

1. An optical system with variable depth of field containing at least one pair or several pairs of lenses, wherein each pair comprises a lens whose transmittance at complex amplitude generates an optical path difference that is equivalent to a surface having a profile, which obeys a symmetric mathematical function. The transmittance in complex amplitude of the other lens of the pair is the conjugate complex of the other element.

2. An optical system with variable depth of field containing at least one pair or several pairs of lenses, wherein each pair comprises a lens whose transmittance in complex amplitude is generated by a surface having a profile, which obeys a mathematical function symmetric The transmittance in complex amplitude of the other lens of the pair is the conjugate complex of the other element. So the surface of the other lens of the pair is the geometric complement to form a block with parallel faces.

3. An optical system with variable depth of field containing at least one pair or several pairs of lenses, wherein each pair comprises a lens with variation of refractive index that is equivalent to a surface having a profile that obeys a mathematical function symmetric and the other lens of the pair obeys a function that is the complex conjugate of the first function.

4. An optical system with variable depth of field containing at least one pair or several pairs of lenses, wherein each pair can comprise a combination of 2 and 3. As claimed in 1, 2, 3 and 4, said system is protected where these lenses can have relative movement between them. As claimed in 1, 2, 3, 4 and 5, said system is protected which may include other types of lenses. As claimed in 1, 2, 3, 4, 5, and 6, said optical system which may include an image processing system is protected. As claimed in 1, 2, 3, 4, 5, 6, and 7, said system is protected which may include at least one positioning system of any of the lenses.