JPH10186231A - How to design a diffractive lens - Google Patents

Abstract

(57) [Problem] A method of designing a fine shape of a diffractive refraction hybrid lens in consideration of light rays other than a light beam parallel to an optical axis has not been known so far. In a method of designing a diffractive lens formed on a lens surface of a refractive lens, a step of expressing an action of the diffractive lens as a function of an optical path difference in a polynomial with a height from an optical axis as a variable; Determining the switching point of the annular zone to be a step based on the function; obtaining the incident angle of the light beam for each annular zone from the macroscopic shape of the diffraction lens; Obtaining the shift in the optical axis direction corresponding to the incident angle, obtaining the optical path difference to be given in each annular zone based on the optical path difference function, and shifting the optical axis direction and the optical path difference. Determining a microscopic shape for each of the annular zones based on

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of designing a diffractive lens suitable for forming a diffractive lens on a lens surface of a refracting lens, and more particularly, to a method for designing a diffractive lens which obliquely enters a general optical axis. The present invention relates to a method for designing a diffractive refraction hybrid lens in a certain case.

[0002]

2. Description of the Related Art In order to correct chromatic aberration with a single lens, there has been conventionally known a lens in which a ring structure having a diffractive lens function is formed on a lens surface which is a curved surface of a refractive lens.
For example, Japanese Patent Application Laid-Open No. 6-242373 discloses an objective lens for an optical disk device in which a diffractive lens structure is formed on the surface of a refractive lens.

In Japanese Patent Application Laid-Open No. Hei 8-171052, a diffractive lens is designed as a thin film having a very high refractive index by a high refractive index method using a sweat model, and a step of an annular zone is provided based on the thin film. A design method is disclosed in which the position and the amount of the step are determined, and the sag amount of the annular zone surface between the steps is obtained as the sum of the sag amount of the base refractive lens and the sag amount of the diffractive lens structure.

[0004]

In addition to the above, there are known several conventional examples of lens design using a diffractive lens. Nothing is known other than those designed for optical disks as in the publication. JP-A-6-242
In the objective lens described in Japanese Patent No. 373, calculation is complicated because an aspheric coefficient is determined for each orbicular zone. Further, in the calculation disclosed in Japanese Patent Application Laid-Open No. H8-171052, the change in the sag amount of the diffractive lens structure in the annular zone is expressed as s (z)-(r
(z) ² -H ² ) ^1/2 , which is defined using a form representing a spherical surface, there is a portion where the power of the diffractive lens is close to 0, that is, a portion where the radius of curvature r is very large. However, the performance is limited because the error is large when performing the calculation and the expression is a quadratic function.
There is a problem that the amount of generated aberration is large as compared with the diffractive lens structure obtained by the method disclosed in JP-A-242373.

The present invention has been made in view of the above-mentioned problems of the prior art, and is not as complicated as determining an aspherical coefficient for each annular zone (disclosed in Japanese Patent Application Laid-Open No. 6-242373). It is possible to suppress the occurrence of aberration due to errors in expression as compared with the method disclosed in Japanese Unexamined Patent Publication No. Hei 8-171052, and to cope with incident light other than a parallel light flux. It is an object of the present invention to provide a method of designing a diffraction lens capable of determining a fine shape that maximizes diffraction efficiency.

[0006]

A method of designing a diffractive lens according to the present invention comprises the steps of expressing the action of a point on a lens surface of the diffractive lens as an added amount of an optical path length to a passing light beam; Calculating the inclination of the surface from the optimal shape, obtaining the cosine of the average incident angle of the light beam incident on a point on the lens surface to be planned, and corresponding to the unit wavelength from the cosine of the average incident angle. Determining the amount of shift of the surface in the optical axis direction to be performed; determining the actual optical path difference amount to be given by the optical axis direction shift of the point based on the added amount of optical path length; and light corresponding to the unit wavelength. Determining a shift amount in the optical axis direction at a point on the lens surface based on the shift amount in the axial direction and the optical path difference.

From another viewpoint, a method of designing a diffractive lens formed on a lens surface of a refractive lens according to the present invention is characterized in that the function of the diffractive lens is a polynomial optical path difference function using a height from an optical axis as a variable. And the step of determining the switching point of the annular zone that becomes a step based on the optical path difference function; the step of determining the angle of incidence of light rays for each annular zone from the macroscopic shape of the diffractive lens; Obtaining a shift in the optical axis direction corresponding to the unit wavelength of the optical path difference for each unit based on the incident angle; obtaining an optical path difference to be given in each annular zone based on the optical path difference function; Determining a microscopic shape for each of the annular zones based on a direction shift and the optical path difference.

[0008]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a diffraction lens designing method according to the present invention will be described below. First, the configuration of a refraction-diffraction hybrid lens on which a target diffraction lens is formed will be described. As described above, the present invention can be applied to a lens having an angle of view (that is, a case where there is a ray obliquely incident on the optical axis). A description will be given of an objective lens for an optical disk device that can be considered to be parallel, and then a general condensing lens for forming an image on a light receiving device such as a CCD.

FIG. 1 shows a diffraction lens 1 to which the present invention is applied.
FIG. The lens 10 is, for example, a condenser lens for forming an image on a light receiving device such as a CCD, or a positive lens used as a pickup objective lens of an optical disk device. 1A is a front view of the lens 10, FIG. 1B is a side view showing a macroscopic shape of the lens 10,
FIG. 2C is a partially enlarged side view showing a microscopic shape of the lens 10.

The lens 10 is a single biconvex lens having two aspherical lens surfaces 11, 12 whose radius of curvature increases from the center toward the periphery when viewed macroscopically. On one lens surface 11 of the lens 10, as shown in FIG. 1A, a diffraction lens having a large number of concentric annular zones centered on the optical axis is formed. The diffractive lens has a step in the optical axis direction at the boundary of each annular zone like a Fresnel lens. The height of the step is determined according to the order and wavelength of the diffracted light to be used. Note that, since the diffractive lens can be set on a curved surface, in this embodiment, one surface of the lens is not made flat in order to form the diffractive lens. In the example shown in FIG. 1, a diffraction lens is provided on the surface on the incident side of the parallel light beam.

Next, a method of designing a diffraction lens as described above will be described. The method of the embodiment is a design method when a Fresnel type diffractive lens is added to the lens surface of a refractive lens that is a curved surface, and more specifically, a macroscopic shape and an optical path difference function obtained by a phase function method, Or the macroscopic shape of the high refractive index thin film layer obtained by the sweat model,
This is a method of obtaining a specific processed shape from the refractive index of the medium that forms the diffraction structure.

As described above, as a method of designing a lens in which diffraction and refraction are mixed, various methods are known as a method of designing by separating a macroscopic shape and the power of a diffraction lens. As a typical method, a high refractive index method and a phase function method using a sweat model are known. The high refractive index method using a sweat model is a model in which the refractive power of a diffractive lens is calculated by replacing it with a thin film-like refractive lens having a macroscopic shape. This method, which is also called an ultra-high index method, gives a very high refractive index to the thin film because the diffraction power is replaced by the refraction power.
The use of the sweat model allows the existing lens design program to handle the diffractive lens. When designing using a sweat model in this design method, there is a step of obtaining an optical path difference function in the middle of the procedure for obtaining the final shape. On the other hand, when designing by the phase function method, the macroscopic shape and the optical path difference function are obtained at the end of the normal design for aberration correction. In the following description, a design procedure will be described by taking as an example the case of designing using a sweat model.

[0013] The design itself of a diffractive lens using a sweat model has been conventionally known, as described in the above-mentioned gazette (Japanese Patent Laid-Open No. Hei 8-171052). However,
Since the data obtained by the sweat model is the macroscopic shape of both surfaces of the thin film, it is necessary to form an annular zone with any pitch and at what steps in order to realize the action of the thin film lens obtained by the sweat model. Goodness cannot be determined only from data obtained using the sweat model. In the present embodiment, a procedure for converting a thin film lens obtained by the sweat model to a diffraction lens having a specific annular zone group will be described.

First, the design of a diffractive lens based on a prerequisite sweat model will be briefly described. When performing ray tracing with a diffractive lens design by a high refractive index method using a sweat model, it is preferable that the refractive index of the thin film representing the diffractive lens is higher. However, in reality, the refractive index is set in consideration of the balance between the reduction of the number of significant digits due to the limit of the calculation accuracy of the software used and the simulation error due to the fact that the refractive index of the model thin film takes a finite value. There is a need. Specifically, the refractive index of the thin film is, for example, 500
The setting is made in accordance with the accuracy of the program between about 1,000,000 and about 1,000,000.

The refractive index n of the thin film in the sweat model
Is preferably defined as n (λ) = λ × C + 1 in order to have a characteristic as a function of the wavelength λ of the light beam used. C
Is an arbitrary constant. As a result, the shift amount of the optical path difference in the wavelength unit with respect to the change in the thickness of the thin film becomes constant regardless of the wavelength. To make the calculation easier to understand, n
It is preferable to set (λ) = λ × 10 ^s +1. Here, s is an arbitrary number determined so that the refractive index n satisfies the above-mentioned refractive index range. For example, if the wavelength λ to be blazed is d-line wavelength 587.56 nm and s is set to 6,
The refractive index of the thin film is 588.56, and the shift amount of the optical path difference per 1 nm of the thickness of the thin film is 1λ. By setting the function in this way, the correspondence between the refractive index and the wavelength can be easily understood by the designer, and the thickness in the direction perpendicular to the surface of the thin film layer and the shift amount of the optical path length can be expressed as a simple relationship. Is done.

Note that "1" in the above equation is the refractive index of air, and that the portion represented as a thin film becomes air when processed into an actual annular structure, that is, the annular structure. Is formed at the interface between the thin film and the lens. When the portion represented as the thin film is filled with the lens material after the actual processing, that is, when the annular structure is formed at the interface between the thin film and the air, the refractive index of the lens is replaced with “1”, For example, “1.5” is used. However, such a difference between the constants is set relatively low refractive index,
The result is affected when the thickness of the thin film expressing the diffraction effect is increased, but is hardly affected when the refractive index of the thin film is set to 10,000 or more.

In designing a diffractive lens using the sweat model, first, it is determined on which surface of the refractive lens the diffractive lens is provided. When a diffraction grating is formed on a certain surface of a lens, which surface is to be formed is determined according to the type of aberration to be corrected by the diffraction lens and in view of the ease of processing. Conventionally, a diffraction grating is generally attached to a flat surface, but if an ultraprecision lathe is used, it is possible to attach a diffraction grating to a spherical surface or an aspherical surface other than a flat surface. In the present embodiment, as described above, the diffraction lens is formed on a curved surface.

In the design based on the sweat model, the diffractive lens is expressed as a thin film, so that the fine shape and power of the diffractive lens do not appear. Therefore, an optical path difference function is created as a step in the process of developing the thin film data obtained by the sweat model into a specific diffraction lens structure. The optical path difference function is a function indicating the optical path difference between a light ray traveling in the thin film and a light ray without the thin film as a variable h, which is a distance h from the optical axis at a point where the light ray enters the thin film. In the sweat model, the difference in the optical path length between the light beam traveling in the thin film and the light beam in the absence of the thin film is the jump value of the optical path length of the diffraction lens. That is, in order to create the optical path difference function, the jump value of the optical path length is obtained. In an optical system that is rotationally symmetric with respect to the optical axis, the position on the lens may be represented only by the distance h from the optical axis, so that the optical path difference is expressed as a function of h.

Light rays incident on the thin film from air or another medium having a refractive index n0 such as a lens at an incident angle θ0 are defined by the law of refraction “n0 · sinθ0 = n1 · sinθ1”.
Accordingly, the light travels through the thin film at the refraction angle θ1. However, in the sweat model, since the refractive index n1 of the thin film is significantly larger than the refractive index n0 of the other medium, the incident angle θ0
Irrespective of the magnitude of the refraction angle, the refraction angle θ1 is almost 0 degrees. That is, light rays incident on the thin film at any angle
In the thin film, the light travels almost along the normal line at the point of incidence. Therefore, the optical path difference function can be obtained by determining the thickness of the thin film at each point in the direction along the normal to the plane on which the light beam enters. Actually, the distance h from the optical axis is different 1
The optical path difference function can be obtained by calculating and calculating the thickness of the thin film along the normal line at a position of about zero, and by approximating the result with a polynomial.

In the design based on the sweat model,
If the lens surface (base curve) of the refractive lens provided with the diffractive lens structure is a curved surface, a higher-order optical path difference component than the order of the function used to define the surface at the time of design occurs. Therefore, the optical path difference function using the sweat model cannot be sufficiently approximated by a quadratic function. It is desirable to approximate with at least a quadratic function, and if possible, an accuracy of about an eighth-order function.

The approximation error of the optical path difference function becomes the wavefront aberration as it is. Most optical systems have a wavefront error of 0.01λ
The degree is considered to be acceptable. In the case of the lens data shown in Tables 1 and 2, the error is 1 / 1000λ at the maximum in the expansion up to the eighth order, and the use of the eighth order function is sufficient in accuracy. In expansion up to the sixth order, the error becomes a maximum of 0.02λ. The maximum error is in this range is the accuracy required for forming a fine shape of the objective lens for an optical disk, and the development up to the fourth order is insufficient in accuracy. The quadratic term P2 of the optical path difference function and the focal length fD of the diffractive lens are represented by wavelengths λ
The following equation is obtained: fD = −l / (2 · P2 · λ)

When the optical path difference function is determined, the distance between the switching point of each ring zone and the optical axis is determined based on the optical path difference function. The switching point may be defined as a position where the optical path length of a light beam transmitted through the thin film becomes an integral multiple of the wavelength as disclosed in the above-mentioned publication, but more generally, the optical path length is set to 2nπ
+ Α (0 rad. <Α <2π rad.), And a point at which the remainder when the optical path length is divided by the wavelength coincides with α may be set as the switching point. When the diffractive lens structure is formed on a curved surface, since the optical path difference function has a higher-order term as described above, if this optical path difference function is used as it is, the calculation formula becomes complicated. In particular, when the optical path difference function is defined by an 8th-order or 10th-order function, it is difficult to solve this and make the optical path difference an integral multiple of the wavelength.

On the other hand, the position of the step of the diffractive lens is important for determining the power of the diffractive lens, but the error of the position of the step does not directly result in wavefront aberration. An error in the position of the step only slightly changes the ratio of the burden of the power diffraction component to the power of the refraction component. That is, the error of the step position has no effect on the blazed wavelength, and means that the component of the wavelength change of the spherical aberration changes in an optical system having a wavelength width. Therefore, when correcting the chromatic aberration change of the spherical aberration to the order of the fourth order, that is, the so-called third order spherical aberration, by the wavefront aberration, it is sufficient to obtain the step position based on the optical path difference function up to the fourth order. Therefore, in the embodiment, when determining the switching point of the annular zone, the optical path difference function is expressed by a quartic function including a quadratic term and a quartic term, and the boundary h is determined by solving the quartic function. Higher-order terms such as sixth-order and eighth-order terms that cannot be expressed by a fourth-order function are taken into consideration when determining the shape of each ring zone, and the position in the optical axis direction is determined.

Since the solution of the quartic function composed of the quadratic and quartic terms can be obtained by the formula of the solution of the quadratic function,
The boundary position can be easily obtained. That is,
Optical path difference functions of different orders are obtained, such as a fourth-order optical path difference function for determining the switching point of the annular zone and an eighth-order optical path difference function for determining the position of each annular zone in the optical axis direction. By using for calculation, the load of calculation can be reduced. Naturally, when it is desired to correct the chromatic aberration change of the spherical aberration of the sixth order or higher by the wavefront aberration, the higher order term is also taken into consideration when setting the step position.

After all, in order to find the switching point of the annular zone, a fourth-order expansion formula that is easy to calculate is used, and if a fine shape is formed from the optical path difference function, the optical path difference function for that purpose is up to the eighth order. Use the expansion formula. Otherwise, it is conceivable to use different orders of the optical path difference function at the time of design, such as designing the surface of each annular zone with a route different from the optical path difference function and achieving phase matching. If the design can be performed without the high-order diffraction effect in design, a small value such that the high-order term of the optical path difference function can be ignored using a high-order aspheric surface in the design data by the high refractive index method It can be designed to be

Next, the diffractive lens structure is replaced with a medium having an actual refractive index from a thin film having a high refractive index to design a Fresnel lens-like annular zone structure. Since the refractive index is low in the actual shape, the incident light does not follow the normal direction as in the description of the thin film, but travels in different directions according to the incident angle. Therefore, since the optical path difference given by the difference in the incident angle will be different, if the incident angle cannot be specified as one, it is necessary to determine the shape of the annular zone in consideration of the diffraction efficiency of off-axis light rays. is there. If the wavelength of the incident light beam has a range, it is necessary to consider the change in diffraction efficiency due to the difference in wavelength.

Although the angle of incidence of the light beam on the diffractive lens structure is determined for the macroscopic shape, the actual annular zone is different from the macroscopic shape as shown in FIG. ,
The angle of incidence on the annular zone will be different from the angle of incidence on the macroscopic shape. In order to ensure accuracy, it is desirable to design the orbicular zone taking into account the change in the incident angle, but when correcting chromatic aberration, the macroscopic shape and the microscopic shape are required. The difference of the incident angle with respect to
Since the degree of incidence is on the order of degrees, the influence of the angle of incidence on the annular zone is small even if the difference in the angle of incidence on the macroscopic shape is ignored. Also, if it is likely to be a size that cannot be ignored,
With respect to the provisional shape determined based on the macroscopic shape, the incident angle can be obtained again to obtain a fine shape.

Next, the diffractive lens designing method of the present invention will be described in more detail using a specific lens configuration.
First, as Embodiment 1, first, an objective lens for an optical disc device in which an incident light beam can be considered to be parallel to the optical axis will be described. The lens of this embodiment is an objective lens for an optical disk, and is a refraction-diffractive hybrid lens in which a diffractive lens is added to a lens surface of a plastic double-sided aspherical lens on which parallel light flux enters.

Table 1 shows a numerical configuration showing the macroscopic shape of the first embodiment. In the table, the portion between the first surface and the second surface is a thin film (high refractive index thin film) indicating a diffractive lens portion represented by an ultra high index lens, and the portion between the second surface and the third surface is plastic refraction. The lens, the fourth surface and the fifth surface indicate the protective layer of the optical disk. The symbol NA in the table is the numerical aperture of the objective lens, f is the focal length of the entire system at a wavelength of 780 nm, r
Is the radius of curvature (unit: mm) at the intersection with the optical axis, d is the surface spacing (unit: mm), and n780 and n830 are 780 n wavelengths, respectively.
m, refractive index at 830 nm. Table 2 shows the conic coefficients K defining the aspherical shapes of the first to third surfaces, and the respective aspherical coefficients A4, A6, A8, and A10 of the fourth, sixth, eighth, and tenth orders.

[0030]

[Table 1]

[0031]

[Table 2] First surface K = -0.5100 A4 = -5.6295 × 10 ^-5 A6 = -1.8850 × 10 ^-4 A8 = 6.1500 × 10 ^-5 A10 = -6.8400 × 10 ^-5 Second surface K = -0.5100 A4 ^{= -5.6800 × 10 -5 A6 = -1.8850} × 10 -4 A8 = 6.1500 × 10 -5 A10 = -6.8400 × 10 -5 third surface K = 0.0000 A4 = 1.6510 × 10 -2 A6 = -4.4810 × 10 - ³ A8 = 4.8930 × 10 ^-4 A10 = -8.8000 × 10 ^-5 Focal length of diffractive lens fdoe = -1 / (2λP2) = 120.465 Focal length of refractive lens fref = r / (n'-n) = 3.704

After the design based on the sweat model is completed as described above, the optical path difference function is obtained as a polynomial based on the data of the thin film, and the height of the step portion of the annular zone from the optical axis is obtained by using this function. Next, the height in the optical axis direction in each annular zone is defined by an approximate expression. The optical path difference function is obtained by approximation by sampling the additional amount of the optical path length for the light passing through the thin film designed by the sweat model at several points on the thin film. Here, as shown below, a fourth-order approximation formula for calculating the height of the step from the optical axis is shown below.

(Equation 15) And a 10th-order approximation formula for obtaining the height in the optical axis direction in the annular zone

(Equation 16) Is defined.

When the additional amount of the optical path length is obtained from the high refractive index thin film, and when the function of a conventional diffraction grating provided on a plane is considered, the optical path difference given by the thin film is not reflected on the optical axis at all positions. It was sufficient to find them as parallel distances. However, in the present invention, since it is assumed that the diffraction grating is formed on a curved surface, it is necessary to calculate the optical path length by tracing a ray and finding an intersection between the ray and the surface. However, when the refractive index of the thin film is extremely large as in the above setting, the refraction angle becomes almost 0 irrespective of the incident angle, and the refracted light beam travels along the normal set to the incident point on the surface. The additional optical path length of the light beam incident on the thin film can be approximated by the value obtained by dividing the thickness of the thin film in the optical axis direction by the cosine of the direction of the normal to the incident point on the light incident side surface of the thin film. it can. This approximation can reduce the amount of calculation.

[0034]

[Table 3] 4th order expansion 10th order P2 -5.3213 -5.3213 P4 -3.1124 × 10 ^-1 -3.2194 × 10 ^-1 P6 1.6828 × 10 ^-2 P8 1.0792 × 10 ^-2 P10 -6.0986 × 10 ^-3

First, the switching position of the ring zone is obtained. In this lens, the switching position of the annular zone is determined based on the optical path difference function φ4 developed in the fourth order in order to correct the wavelength change of the spherical aberration. Table 4 below shows the height hi (N) of the center-side end of the Nth orb from the center from the optical axis, the height hc (N) from the optical axis of the center point of the orb, and the orb. The height ho (N) from the optical axis of the edge on the most peripheral side is shown for each orbicular zone. These values are

[Equation 17]

(Equation 18)

[Equation 19] Is required in accordance with

In the case of designing by the phase function method, when there is no higher-order optical path difference function, or when it is not necessary to correct the wavelength change of the spherical aberration, the switching position of the annular zone can be obtained by the quadratic function. Good.

[0037]

[Table 4]

Next, the macroscopic shape of the boundary surface between the thin film and the refractive lens determined by the aspheric coefficient is determined for the center side end, the center, and the peripheral side end of each orbicular zone. The macroscopic shape is

(Equation 20) Is calculated by The calculation result is as shown in Table 5, and is defined as a continuous rotationally symmetric surface without a step.

[0039]

[Table 5]

Subsequently, the angle of incidence of the light beam on each of the zones determined from the macroscopic shape is obtained.

The first derivative dXo depending on the height h of the macroscopic shape
(N) / dh, and based on this,

(Equation 21) , The optical axis direction component L of the direction cosine is obtained, and the angle α (r
ad.)

(Equation 22) Is determined using

In this example, the incident light basically emits only parallel rays adjusted in parallel to the optical axis. Therefore, the angle W at which the incident light forms the optical axis at any point on the lens is 0 rad. is there. Therefore, the incident angle θ (rad.) At each point determined by W−α is as shown in Table 6. Here, since the actual diffraction lens surface has not been determined, the angle θ is calculated using a macroscopic shape. Table 7 shows each value at the end of the outer peripheral portion of each ring zone.

[0043]

[Table 6]

The cosine of the refraction angle is calculated based on the incident angle θ, and the cosine of the refraction angle is calculated using the refractive index of the actual material. Based on these, the optical path difference of 1λ along the normal direction is calculated. Gives the thickness Δt,

(Equation 23) Is calculated by n0 is the refractive index of the medium on the incident side from the diffraction lens surface, and n1 is the refractive index of the medium on the exit side. Also,
In order to convert this step into a step ΔX in a direction parallel to the optical axis, the angle between the optical axis and the normal to the surface is α, and ΔX =
Δt / cosα. In the optical system of this embodiment in which the light beam is parallel to the optical axis, cosα = cosθ. The results of these calculations are as shown in Table 7.

[0045]

[Table 7]

The result calculated by substituting the distance from the optical axis at the center of each zone determined from the fourth-order optical path difference function φ4 into the tenth-order optical path difference function φ10 is φc (N). Table 8 shows the optical path difference between the case where the thin film having the high refractive index set by the sweat model is provided and the case where the thin film is not provided, using the wavelength λ as a unit. φi (N) -N, φc (N)-
N, φo (N) -N are integers of wavelength from the result calculated by substituting the distance from the optical axis at the center end, the center, and the peripheral end into the 10th-order optical path difference function φ10, respectively. In the case where the thin film represented by the continuous optical path difference function φ10 is divided into a plurality of Fresnel lens-shaped orbicular zones by providing a step at the position determined from the fourth-order optical path difference function φ4. It shows the amount of optical path difference to be added by a fine shape with respect to the macroscopic shape of the center side end point, the center portion, and the peripheral side end point in each ring zone. If, for example, a position where the optical path length difference has a decimal part of 0.5λ just is searched for without forming an approximation function from the sample point, the optical path length difference to be formed into a fine shape is obtained. Although there is no longer a small significant figure as shown in Table 8, it is not very meaningful because the calculation amount is increased.

[0047]

[Table 8]

The product of the above-described calculation result of the tenth-order optical path difference function and the thickness ΔX in the optical axis direction corresponding to one wavelength for each ring zone is obtained, so that each position of each ring zone is obtained. An amount obtained by converting a necessary optical path difference in the optical axis direction into a lens thickness of an actual shape is obtained. That is, ΔX is the thickness in the optical axis direction corresponding to one wavelength at the peripheral end portion of each annular zone, and φX shown in the above table
Since o (N) -N specifies a surplus that is less than one wavelength, the lens thickness in the optical axis direction necessary for the surplus can be obtained by multiplying the surplus. Note that ΔX shown in Table 8 is a value at the peripheral end portion. In order to obtain the step at the center end, the value of ΔX of one center side annular zone may be referred to. Further, in order to obtain the optical path difference at the center, the average value of the ΔX values of the zones before and after sandwiching the center is used without making ΔX for the center of the zone not shown in Table 8. However, a design with sufficient accuracy is possible. Table 9 shows the lens thicknesses ΔXi (N), ΔXc (N), and ΔXo (N) of the optical path difference between the inner end, the center, and the outer end of each annular zone.

[0049]

[Table 9]

The actual shape is obtained from the lens thickness data corresponding to the added optical path difference and the macroscopic shape shown in Table 5. Table 10 shows the shape data. this is,
This is sag amount data provided in a state that also includes information on a macroscopic shape, that is, a base curve.

[0051]

[Table 10]

When a diffractive lens (or a mold thereof) is manufactured using an ultra-precision lathe, data at each point on the annular zone as shown in Table 10 above is obtained for every bite feed pitch. Although data can be created, in order to reduce the amount of calculation, it is desirable that the feed trajectory of the byte can be approximated and represented by a function. Therefore, in this embodiment,
The lens thickness of the optical path difference at the three points obtained for each of the above annular zones is approximated by a fourth-order polynomial as a function, and the 0th-order, 2nd-order,
Next, a fourth-order coefficient is obtained, and the byte feed amount is controlled based on the fourth-order approximate polynomial. The coefficient of the quartic function (Equation 3) passing through three points is

(Equation 24)

(Equation 25)

(Equation 26) Required by Table 11 is a list of calculation results of the respective coefficients when the amount of the fine structure portion sag added to the macroscopic shape is approximated by a quartic function.

[0053]

Table 11 zonal number 0 order coefficient secondary coefficient fourth order coefficient N B0N B2N B4N 0 0.0000000 0.0078084 0.0000000 1 -0.0014530 0.0076664 8.1589 × 10 -4 2 -0.0029055 0.0075970 8.1963 × 10 -4 3 -0.0043565 0.0075236 8.2380 × 10 - ⁴ 4 -0.0058041 0.0074423 8.3127 × 10 ^-4 5 -0.0072445 0.0073468 8.4465 × 10 ^-4 6 -0.0086709 0.0072284 8.6631 × 10 ^-4 7 -0.0100739 0.0070768 8.9841 × 10 ^-4 8 -0.0114404 0.0068804 9.4294 × 10 ^-4 9 -0.0127538 0.0066260 1.0018 × 10 ^-3 10 -0.0139939 0.0062997 1.0766 × 10 ^-3 11 -0.0151366 0.0058864 1.1689 × 10 ^-3 12 -0.0161542 0.0053708 1.2802 × 10 ^-3 13 -0.0170157 0.0047370 1.4118 × 10 ^-3 14 -0.0176866 0.0039694 1.5646 × 10 ^-3 15 -0.0181305 0.0030526 1.7394 × 10 ^-3 16 -0.0183088 0.0019726 1.9368 × 10 ^-3 17 -0.0181828 0.0007165 2.1570 × 10 ^-3 18 -0.0177141 -0.0007263 2.3998 × 10 ^-3

From the coefficients shown in Table 11, r in Table 1, aspherical coefficients in Table 2, and (Equation 3), the macroscopic shape (sag amount) X for an arbitrary h (height from the optical axis) is calculated. You can ask.

Further, the entire fine shape is represented by a quartic function for each ring zone,
Alternatively, it can be expressed as a quadratic function. 4
When expressed by the following function,

[Equation 27] In this case, the coefficients C0N, C2N, and C4N are obtained by (Equation 12), (Equation 13), and (Equation 14), respectively. Table 12 shows the calculation results of the coefficients.

[0056]

Table 12 zonal number 0 order coefficient secondary coefficient fourth order coefficient N C0N C2N C4N 0 0.0000000 0.2600433 0.0000 1 -0.0014699 0.2593101 8.3768 × 10 -03 2 -0.0029527 0.2592799 8.5535 × 10 -03 3 -0.0044402 0.2591988 8.7190 × 10 - ⁰³ 4 -0.0059338 0.2590979 8.8560 × 10 ^-03 5 -0.0074489 0.2590228 8.9489 × 10 ^-03 6 -0.0090184 0.2590305 8.9843 × 10 ^-03 7 -0.0106940 0.2591865 8.9506 × 10 ^-03 8 -0.0125474 0.2595632 8.8375 × 10 ^-03 9 -0.0146709 0.2602377 8.6361 × 10 ^-03 10 -0.0171770 0.2612905 8.3386 × 10 ^-03 11 -0.0201975 0.2628044 7.9383 × 10 ^-03 12 -0.0238835 0.2648633 7.4296 × 10 ^-03 13 -0.0284035 0.2675516 6.8074 × 10 ^-03 14 -0.0339428 0.2709531 6.0678 × 10 ^-03 15 -0.0407016 0.2751505 5.2073 × 10 ^-03 16 -0.0488942 0.2802252 4.2230 × 10 ^-03 17 -0.0587470 0.2862561 3.1128 × 10 ^-03 18 -0.0704971 0.2933200 1.8751 × 10 ^-03

A macroscopic shape (sag amount) X for an arbitrary h (height from the optical axis) can be obtained based on each coefficient shown in Table 12 and (Equation 27). Note that the entire fine shape can be expressed by a quadratic function for each wheel pair. Here, the quadratic function is a function represented by (Equation 2). (Equation 2)
The coefficients C0N and C2N when expressed by the function of
0) and (Equation 11).

Next, as a second embodiment, an example will be described in which the present invention is applied to a general lens having an angle of view (that is, a case where a light beam obliquely enters the optical axis). The lens of Example 2 is a lens for forming an image of visible light on a light receiving device having a small light receiving area, such as a CCD, and diffracts into a lens surface on the side where a light beam of a glass double-sided aspherical lens is incident. This is a refraction-diffraction hybrid lens with a lens added. A plane-parallel plate-shaped medium exists on the image forming surface side of the condenser lens. Table 14 shows a numerical configuration showing a macroscopic shape of the second embodiment. This lens is designed using an optical path difference function and has no ultra high index data. The first surface 11M is a diffractive refraction hybrid surface,
Between the first surface 11M and the second surface 12M, a plastic refracting lens 10M is shown, and the third to sixth surfaces show two parallel flat plates 21, 22 (see FIG. 3).

In Table 13, f is the wavelength of the d-line (587.56
nm) focal length of the whole system (unit: mm), W is half angle of view, r
Is the radius of curvature (unit: mm) at the intersection with the optical axis, d is the surface interval (unit: mm), nd is the refractive index at the d-line (wavelength: 587.56 nm), and νd is the Abbe number. Table 14 shows the conical coefficients K and the fourth, sixth, eighth, and tenth order aspherical coefficients that define the aspherical shapes of the first and second surfaces.

[0060]

[Table 13]

[0061]

[Table 14] Surface 1 K = 0.00 A4 = 1.350 × 10 ^-3 A6 = 2.600
× 10 ^-4 A8 = -3.0500 × 10 ^-5 A10 = 1.3800 × 10 ^-5 Second surface K = 0.00 A4 = 8.900 × 10 ^-3 A6 = 2.920 × 10 ^-3 A8
= -1.0300 × 10 ^-3 A10 = 6.7800 × 10 ^-4 Focal length of diffractive lens fdoe = -1 / (2λP2) = 7
0.457 Blaze wavelength 570nm

First, the switching position of the annular zone is determined based on the optical path difference function φ8 used up to the eighth order. The optical path difference function φ8 is

[Equation 28] Shown in When the optical path difference function φ8 is used, unlike the quartic function, the switching position is calculated repeatedly to obtain the switching position, but the calculation can be performed with sufficient accuracy.

Table 15 below shows the height hi (N) of the center-side end of the Nth orb from the center from the optical axis, and the height hc (N) of the central point of the orb from the optical axis. The height ho (N) of the most peripheral end of the orb from the optical axis is shown for each orb. These values are
It is obtained by repeated calculations such as Newton's method.
However, the effective radius of the first surface is 2.2 mm, and the total number of orbicular zones is 70. Therefore, in Table 15, the intermediate orbicular zones are partially omitted.

[0064]

[Table 15]

Next, the macroscopic shape of the diffractive refraction hybrid surface determined by the aspherical coefficient is determined for the center-side end, the center, and the peripheral end of each orbicular zone. The macroscopic shape is calculated by (Equation 20). Table 1 shows the calculation results.
6 and is defined as a continuous rotationally symmetric surface without any steps.

[0066]

[Table 16]

Subsequently, the angle of incidence of the light beam on each of the zones determined from the macroscopic shape is determined. The first derivative dXo (N) / dh based on the height h of the macroscopic shape is obtained, and based on this, the optical axis direction component L of the direction cosine is obtained according to (Equation 21), and the surface of the surface defined by the macroscopic shape is determined. The angle α (rad.) With respect to the optical axis is determined using (Equation 22). In this example, since the angle W formed by the incident light beam with the optical axis changes depending on the angle of view, an average incident angle is considered. If the beam angle and the angle of view are too large to determine the angle of incidence with one ray,
The fine shape is determined by using the average incident angle of the light beam incident on the surface.

To increase the diffraction efficiency on average, (1) a method of averaging the minimum value and the maximum value of the absolute value of the incident angle,
(2) a method of taking the absolute value of the incident angle in consideration of the image area, and (3) a method of taking the mean of the square of θ in consideration of the image area, etc. In the present embodiment, since the thickness of the step to be finally determined changes with the square of the incident angle, a method of determining the incident angle by the average of the square of the incident angle is adopted.

A method using the mean square incident angle will be described. The distribution of light rays incident on one point on the lens (effectively contributing to imaging) cannot be easily determined. However, since it is troublesome to find the incident angle for each point, the step at each point is determined by a simple calculation under a rather rough assumption. Here, the following assumptions are made. (1) A light beam incident on one point becomes a perfect conical area. (2) The distribution of incident angles is equally spaced on concentric circles. Assuming that the above assumptions hold, in the sum of squares,
The average incident angle will be determined.

Note that it is not impossible to obtain the average incident angle with almost no approximation by using current design tools. However, when the image plane that is effectively used is rectangular, as in a photographic lens, the incident angle distribution differs for each image height direction, and the rotational symmetry of the plane is lost, so the amount of computation explodes. Will increase. In contrast, most lenses with an actual angle of view and luminous flux width also have a wavelength width in most cases, so the contribution to diffraction efficiency due to the change in incident angle due to increased calculation accuracy is buried in the loss due to the wavelength characteristic term. You don't need to calculate that exactly. Under the above approximation, the simple average incident angle is m, the half value of the angular width is r, and the square mean incident angle is U,

(Equation 29) Holds.

In (Equation 29), r and m can be obtained as follows. (1) The maximum ray angle θU and the minimum ray angle θL that can be incident with respect to the height h of the surface in the meridional section are obtained by ray tracing. (2) By converting θU and θL into a function of h, for any h, θ
U and θL are determined. (3) m = ((θU + θL) / 2−normal angle α of surface) r = ((θU−θL) / 2)

As a result of such calculation, the root mean square incident angle θ (rad.) At each point is as shown in Table 17. Here, similarly to the first embodiment, since the actual diffraction lens surface is not determined, the angle θ is calculated using a macroscopic shape.

[Table 17] Ring number No. 1st derivative Angle of direction cosine plane Mean square incident angle N dXo / dh L α (rad.) Θ 0 0.0609 0.9982 0.0608 0.2971 1 0.1059 0.9944 0.1056 0.2977 2 0.1374 0.9907 0.1365 0.3035 3 0.1632 0.9869 0.1618 0.3099 4 0.1859 0.9832 0.1838 0.3165 5 0.2065 0.9793 0.2036 0.3229 6 0.2255 0.9755 0.2218 0.3293 7 0.2433 0.9717 0.2387 0.3354 8 0.2602 0.9678 0.2546 0.3414 9 0.2764 0.9639 0.2696 0.3472 10 0.2919 0.9599 0.2840 0.3528 11 0.3069 0.9560 0.2978 0.3582 12 0.3215 0.9520 0.3111 0.3633 13 0.3 0.3683 14 0.3497 0.9440 0.3364 0.3730 15 0.3633 0.9399 0.3485 0.3775 16 0.3767 0.9358 0.3603 0.3818 17 0.3899 0.9317 0.3718 0.3859 18 0.4030 0.9275 0.3831 0.3899 19 0.4158 0.9233 0.3941 0.3936 20 0.4286 0.9191 0.4049 0.3971 21 0.4412 0.9149 0.4155 0.4005 22 0.4538 0.9106 0.4260 0.4037 23 0.4663 0.906 0.4363 0.4067 24 0.4787 0.9020 0.4465 0.4096 25 0.4911 0.8976 0.4565 0.4123 26 0.5034 0.8932 0.4664 0.4149 27 0.5158 0.8888 0.4762 0.4173 28 0.5281 0.8843 0.4859 0.4196 29 0.5404 0.8797 0.4955 0.4217 30 0.5528 0.8752 0.5050 0.4237 35 0.6152 0.8517 0.5515 0.4321 40 0.6796 0.8271 0.5969 0.4381 45 0.7471 0.8011 0.6416 0.4424 50 0.8188 0.7737 0.6861 0.4455 55 0.8957 0.7449 0.7304 0.4480 60 0.9790 0.7146 0.7748 0.4502 65 1.0696 0.6829 0.8190 0.4523 70 1.1686 0.6502 0.8630 0.4544

The cosine of the refraction angle is calculated based on the incident angle θ, the cosine of the refraction angle is calculated using the refractive index of the actual material, and the thickness Δt along the normal direction is calculated based on these. It is calculated by equation (23). In order to convert this step into a step ΔX in the direction parallel to the optical axis, ΔX = Δt / cos α, where α is the angle between the optical axis and the normal to the surface. The results of these calculations are as shown in Table 18.

[0074]

[Table 18] Zone number N cosθ cosθ '△ t △ X 0 0.9562 0.9868 -0.0006908 -0.0006921 1 0.9560 0.9867 -0.0006908 -0.0006946 2 0.9543 0.9862 -0.0006901 -0.0006966 3 0.9523 0.9856 -0.0006893 -0.0006985 4 0.9503 0.9850 -0.0006886 -0.0007004 5 0.9483 0.9844 -0.0006878 -0.0007023 6 0.9463 0.9838 -0.0006870 -0.0007042 7 0.9443 0.9832 -0.0006862 -0.0007062 8 0.9423 0.9826 -0.0006854 -0.0007083 9 0.9403 0.9821 -0.0006847 -0.0007104 10 0.9384 0.9815 -0.0006840 -0.0007125 11 0.9365 0.9810 -0.0006832 -0.0007147 12 0.9347 0.9804 -0.0006825 -0.0007169 13 0.9330 0.9799 -0.0006818 -0.0007193 14 0.9312 0.9794 -0.0006812 -0.0007216 15 0.9296 0.9789 -0.0006805 -0.0007241 16 0.9280 0.9785 -0.0006799 -0.0007266 17 0.9264 0.9780 -0.0006793 -0.0007292 18 0.9250 0.9776 -0.0006788 -0.0007318 19 0.9235 0.9772 -0.0006782 -0.0007345 20 0.9222 0.9768 -0.0006777 -0.0007373 21 0.9209 0.9764 -0.0006772 -0.0007402 22 0.9196 0.9760 -0.0006767 -0.0007431 23 0.9184 0.9757 -0.0006763 -0.0007462 24 0.9173 0.975 4 -0.0006758 -0.0007493 25 0.9162 0.9750 -0.0006754 -0.0007524 26 0.9152 0.9748 -0.0006750 -0.0007557 27 0.9142 0.9745 -0.0006746 -0.0007591 28 0.9133 0.9742 -0.0006743 -0.0007625 29 0.9124 0.9740 -0.0006739 -0.0007661 30 0.9116 0.9737 -0.0006736 -0.0007697 35 0.9081 0.9727 -0.0006723 -0.0007893 40 0.9056 0.9720 -0.0006713 -0.0008117 45 0.9037 0.9715 -0.0006706 -0.0008371 50 0.9024 0.9711 -0.0006701 -0.0008661 55 0.9013 0.9708 -0.0006697 -0.0008991 60 0.9004 0.9705 -0.0006693 -0.0009367 65 0.8995 0.9703 -0.0006690 -0.0009796 70 0.8985 0.9700 0.0006686 -0.0010284

As described above, in the second embodiment, the boundary point of the ring zone is determined by using the eighth-order optical path difference function itself obtained at the time of design. Part, phase deviation from the macroscopic shape at the peripheral end φi (N) -N, φ
c (N) -N, φo (N) -N are 0.500λ, 0λ, -0.500λ, respectively.
It has become. Table 19 shows the results.

[0076]

[Table 19]

By taking the product of the thickness ΔX in the optical axis direction corresponding to one wavelength for each annular zone and ± 0.5, the optical path difference in the optical axis direction required at each position of each annular zone is formed in the actual shape. Calculated as the fine shape converted to The results are shown in Table 20.

[0078]

[Table 20]

From the optical path difference data and the macroscopic shape shown in Table 16, the actual shape required to give the above optical path difference is determined. Table 21 shows the shape data. This is the data of the sag amount provided in a state including the information of the macroscopic shape, that is, the base curve.

[0080]

[Table 21]

Also in this example, the lens thickness of the optical path difference of the three points obtained for each of the above-mentioned zones is approximated by a fourth-order polynomial as a function, and zero-order, second-order, and fourth-order coefficients are obtained. However, in the case of the second embodiment, since the number of zones is large, the width of each zone is narrow, and even if approximated by a quadratic equation, the error is at most 1 / 300λ. It can be approximated to the following sufficient accuracy. The quadratic function is represented by (Equation 1), and the coefficients B0N and B2N in this case are obtained by (Equation 5) and (Equation 6), respectively. Table 22 is a list of the calculation results of the coefficients B0N and B2N.

[Table 22]

Data of the sag amount X with respect to an arbitrary height h can be obtained from r shown in Table 13, the aspheric coefficient shown in Table 14, and B0N and B2N shown in Table 22 (Equation 1).

Further, as in the case of the first embodiment, the entire fine shape can be expressed as a quadratic function for each ring zone. The quadratic function in this case is represented by (Equation 2), and the coefficients C0N and C2N are obtained by (Equation 10) and (Equation 11), respectively. The coefficients thus calculated are shown in Table 23.

[0084]

[Table 23]

Accordingly, each coefficient shown in Table 23 and (Equation 3)
0), a macroscopic shape (sag amount) X for an arbitrary h (height from the optical axis) can be obtained.

[0086]

As described above, according to the method for designing a diffractive lens of the present invention, it is possible to easily design the boundaries and steps of the annular zone of the diffractive lens based on the output of an automatic design program based on a sweat model or the like. In addition, the accuracy of the performance of the diffraction lens can be kept high.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram of a refraction-diffraction hybrid lens to which a design method of the present invention is applied.

FIG. 2 is a lens diagram of an objective lens according to an example.

FIG. 3 is a lens diagram of a condenser lens according to a second embodiment.

[Explanation of symbols]

 10 Objective lens 11,12 Lens surface 10M Condensing lens 11M, 12M Lens surface

[Equation 30]

Claims (19)

[Claims] 1. A method of designing a fine shape of a diffractive lens formed on a lens surface of a refracting lens, wherein the step of expressing a function of the diffractive lens at a point on the lens surface as an optical path length addition amount to a passing light beam; Obtaining the surface inclination from the macroscopic shape of the lens; obtaining the cosine of the average incident angle of the light beam incident on the point on the predetermined lens surface; and calculating the unit from the cosine of the average incident angle. Obtaining a shift amount of the surface in the optical axis direction corresponding to the wavelength component; obtaining an actual optical path difference amount to be given by the optical axis direction shift of the point based on the optical path length addition amount; Determining the amount of shift in the optical axis direction at a point on the lens surface based on the shift amount in the optical axis direction and the optical path difference corresponding to How to design a lens. 2. A method of designing a diffractive lens formed on a lens surface of a refracting lens, wherein the function of the diffractive lens is represented as a polynomial optical path difference function using a height from an optical axis as a variable; Determining the switching point of the annular zone to be a step based on the function; obtaining the incident angle of the light beam for each annular zone from the macroscopic shape of the diffractive lens; Obtaining a shift in the optical axis direction corresponding to the angle of incidence based on the incident angle; obtaining an optical path difference to be given in each annular zone based on the optical path difference function; and shifting the optical axis direction and the optical path difference. Determining a microscopic shape for each of the orbicular zones based on the following formula: 3. The method according to claim 2, wherein the step of obtaining the incident angle includes the step of obtaining an average incident angle of light rays from design data. 4. The step of obtaining the average incident angle,
The method of designing a diffraction lens according to claim 3, wherein the step is a step of obtaining a square mean incident angle of the incident angle. 5. The method according to claim 2, wherein the step of determining the microscopic shape includes the step of approximating the microscopic shape by a second-order polynomial. . 6. The method according to claim 2, wherein the step of determining the microscopic shape includes the step of approximating the microscopic shape with a fourth-order polynomial. . 7. The optical path difference function includes a first approximate expression for determining a switching point of the orb, and a first polynomial for determining a shift in an optical axis direction for each of the orb. The method according to claim 2, further comprising a second approximate expression having a higher order. 8. The method according to claim 7, wherein the first approximate expression is a fourth-order polynomial, and the second approximate expression is at least an eighth-order polynomial. . 9. The method according to claim 8, wherein the second approximate expression is a 10th-order polynomial. 10. The method of designing a diffractive lens according to claim 1, wherein the action of the diffractive lens is obtained by a high refractive index method using a sweat model. 11. A second-order polynomial for approximating the microscopic shape is expressed by the following equation, including the surface shape of the refractive lens. The method for designing a diffractive lens according to claim 5, wherein: 12. A second-order polynomial for approximating the microscopic shape is expressed by the following equation, including the surface shape of the refractive lens. The method for designing a diffractive lens according to claim 5, wherein: 13. A fourth-order polynomial for approximating the microscopic shape is expressed by the following equation, including the surface shape of the refractive lens. The method for designing a diffractive lens according to claim 6, wherein: 14. A fourth-order polynomial for approximating the microscopic shape is expressed by the following equation, including the surface shape of the refractive lens. The method for designing a diffractive lens according to claim 6, wherein: 15. The polynomial for approximating the microscopic shape utilizes symmetry of the microscopic shape with respect to the optical axis for each of the annular zones, and passes through at least two points having different heights from the optical axis. The method of designing a diffractive lens according to claim 5, wherein the method is defined as a trajectory. 16. The coefficients defining the second-order polynomial diffractive lens may be defined by a point in the optical axis direction at each of the most central point and the most peripheral point of the Nth orbicular zone counted from the optical axis. The shift amounts are △ Xi (N) and △ Xo (N), and the distances of the points from the optical axis are hi (N) and ho (N), respectively. (Equation 6) 12. The method for designing a diffractive lens according to claim 11, wherein the method is obtained by the following. 17. The coefficients defining the fourth-order polynomial diffractive lens are the light at each of the most central point, the center point, and the most peripheral point of the Nth orbicular zone counted from the optical axis. The amount of shift in the axial direction is △ Xi (N), △ Xc (N), △ Xo (N), and the distance from the optical axis of each point is hi (N), hc (N), ho (N). , (Equation 8) (Equation 9) 14. The method for designing a diffractive lens according to claim 13, wherein: 18. The coefficients defining the second-order polynomial diffractive lens may be defined by a point in the optical axis direction at each of the most central point and the most peripheral point of the Nth orbicular zone counted from the optical axis. Let Xi (N) and Xo (N) be the positions and hi (N) and ho (N) be the distances from the optical axis of each point, respectively. [Equation 11] 13. The method of designing a diffractive lens according to claim 12, wherein the method is obtained by the following. 19. The coefficients defining the fourth-order polynomial diffractive lens are the light at each of the most central point, the central point, and the most peripheral point of the Nth orbicular zone counted from the optical axis. The positions in the axial direction are Xi (N), Xc (N), Xo (N), and the distances of the points from the optical axis are hi (N), hc (N), ho (N), respectively. ] (Equation 13) [Equation 14] 15. The method for designing a diffractive lens according to claim 14, wherein: