Meta Patent | Optical components having athermalization and aberration correction characteristics

In some examples, L₀ may be the nominal barrel length at an particular temperature (e.g., 20 degrees) and α_barrel may be a coefficient of thermal expansion (CTE) of the barrel material.

Also, in some examples, a focal length shift with respect to temperature Δf(T) may be equal to a difference of the focal length and a length of a lens barrel, and may be calculated as follows:

Δ⁢f⁡(T)=f⁡(T)-L⁡(T)=f0*(1+(αlens-dnTdTn0-1)*Δ⁢T)-L0*(1+αb⁢a⁢r⁢r⁢e⁢l*Δ⁢T).

It should be appreciated that defocus Δf(T) may be minimized where a nominal barrel length L₀ may be close or equal to a nominal focal length f₀. In these instances, the defocus Δf(T) equation may can be further simplified (i.e., approximated) as follows:

Δ⁢f⁡(T)≈f0⁢Δ⁢T⁡((αlens-dnTdTn0-1)-αbarrel).

Furthermore, a calculation of defocus Δf(T) may again be simplified if a lens barrel may have a same or similar coefficient of thermal expansion (CTE) as a lens. In some instances, a nominal focal length of a lens may be approximately equal to a lens barrel length at a nominal temperature. In these instances, a “telephoto ratio” (i.e., a ratio of the nominal focal length of a lens and a lens barrel length at a nominal temperature) may be approximately equal to one. Where a telephoto ratio may be approximately equal to one, the defocus Δf(T) may be simplified as follows:

Δ⁢f⁡(T)≈f0⁢Δ⁢T*(-dnTdTn0-1).

From the above equation, it should be appreciated that defocus Δf(T) may be proportional to a nominal focal length f₀ of a lens and a derivative dn_T/dT of a refractive index relative to temperature T. Furthermore, it should also be appreciated that Δf(T) may be inversely proportional to the refractive index of a lens material at nominal temperature n₀. Accordingly, it may follow that to design a lens minimally sensitive to temperature, it may be desirable to utilize a lens having a small(er) focal length f₀ that be made of a material having a small(er) derivative dn_T/dT of the refractive index relative to temperature T and a large(r) refractive index n₀.

Focal Shift Characteristics in a Plastic Singlet

In some examples, a simple lens or “singlet” may be analyzed to determine optical characteristics. FIG. 1 illustrates a block diagram of a singlet 100. FIG. 2 illustrates a table of specifications that the singlet 100 may utilize. These specifications may include wavelength, focal length, F# (described further below), lens format, lens material and lens barrel material. In some examples, the singlet 100 may include a lens barrel 105.

So, in these examples, it may be observed that over a temperature change from −25° C. to 85° C., if the coefficient of thermal expansion (CTE) of the lens barrel material may be 285×10e⁻⁶ (m/mK⁻¹), the singlet 100 may have very small focal shift (<1.0 um). In addition, in some examples, it may also be observed that a focal shift of the singlet 100 may exceed an expansion of the lens barrel 105 when the temperature may remain above (a nominal) 20° C. Furthermore, in some examples, the focal shift of the singlet 100 may (inversely) remain shorter than that of the lens barrel 105 when the temperature may drop below the (nominal) 20° C. Accordingly, in some examples, a focal shift Δf(T) as a function of temperature T may be calculated as follows:

Δ⁢f⁡(T)≈f0⁢Δ⁢T*(-dnTdTn0-1).

It should be appreciated that, in these examples, the focal shift Δf(T) of the singlet 100 may be related to the derivative dn_T/dT of the refractive index relative to temperature T.

It the case of glass (e.g., BK7), it should be appreciated that in some examples, a glass singlet may have a much smaller focal shift than that of a plastic singlet. In these examples, this may be so because the glass singlet may have a smaller coefficient of thermal expansion (CTE) than that of a lens barrel material and may have a small (and positive) derivative dn_T/dT of the refractive index relative to temperature T. Accordingly, in some examples, a focal shift for a glass singlet may be calculated as follows:

Δ⁢f⁡(T)≈f0⁢Δ⁢T⁡((αlens-dnTdTn0-1)-αbarrel).

Furthermore, in some examples, since the derivative dn_T/dT of the refractive index relative to temperature T of the glass singlet may positive when temperature may increase, the focal shift Δf(T) of the glass singlet may decrease. In some examples, this may mean that a focal length shift caused by a coefficient of thermal expansion (CTE) and a focal shift caused by a derivative dn_T/dT of the refractive index relative to temperature T may be opposed, and therefore may neutralize each other. For at least this reason, focal shift in a glass singlet may typically be less than in a plastic singlet.

Athermalization Characteristics for a Plastic Lens

Various properties of plastic may be utilized to achieve athermalization of a plastic lens. For example, for at least the reasons discussed above, athermalization in a plastic lens may require a barrel having a larger (an often significantly larger) barrel than that of a glass lens. Indeed, in some examples, it may be observed that a plastic material used for a lens may require a coefficient of thermal expansion (CTE) above 285×10⁻⁶/T⁻¹. That is, in some instances, a plastic singlet may require a large(r) coefficient of thermal expansion (CTE) of a lens barrel to achieve athermalization. Unfortunately, however, in some instances, it may be difficult to secure plastic that may possess such a large coefficient of thermal expansion (CTE).

In some examples, one way to compensate for a large focal shift generated by a plastic lens may be to increase a barrel length. Moreover, in some examples, to compensate for a large focal shift provided by use of a plastic lens, a second barrel with a different coefficient of thermal expansion (CTE) may be utilized. These configurations may also be referred to as a “barrel-in-barrel” or “multi-barrel” configuration. A first example of a barrel-in-barrel configuration 305 is shown in FIG. 3A, and a second barrel-in-barrel configuration 310 is shown in FIG. 3B. In some instances, such barrel-in-barrel configurations may compensate for a focal shift by holding an image sensor in position at a correct focal plane.

In some examples, to achieve athermalization, the following design considerations may be provided. First, a first barrel may require a larger coefficient of thermal expansion (CTE) and a second barrel may require a smaller coefficient of thermal expansion (CTE). Next, in an instance where a coefficient of thermal expansion (CTE) of second barrel may be zero, a length of a first barrel may need to be longer (e.g., approximately 4-5× longer) than a focal length that which may be provided by use of a single barrel with having a high coefficient of thermal expansion (CTE). Also, in examples where a second barrel may exhibit negative expansion (i.e., the barrel may shrink as temperature may rise), a length of a first barrel may be made shorter. Furthermore, if a telephoto ratio may be less than one, a lens barrel may require a large coefficient of thermal expansion (CTE) (e.g., >285×10e⁻⁶), and a second barrel may not be required.

Athermalization Characteristics of a Glass Lens

In some examples, a glass lens may be configured for athermalization as well. Similar to the example of the plastic singlet described above, a glass lens may utilize a barrel-in-barrel configuration. Moreover, in some examples, a material of an inside barrel of a barrel-in-barrel configuration may be chosen having a small(er) coefficient of thermal expansion (CTE). In these examples, an outside barrel of the barrel-in-barrel configuration may be chosen having a small(er) coefficient of thermal expansion (CTE) material as well. In other examples, a material of an inside barrel of a barrel-in-barrel configuration may be chosen having a large(r) coefficient of thermal expansion (CTE). In these examples, an outside barrel of the barrel-in-barrel configuration may be chosen having a large(r) coefficient of thermal expansion (CTE) material as well. In some examples this may be because, as discussed above, glass may have a small(er) variation in focal shift with respect to a change in temperature. It should further be appreciated that, as a glass lens may not be as sensitive to a change in temperature, a telephoto ratio of less than one may be easier to achieve. Furthermore, in some examples, athermalization in a glass singlet may be easier as glass may typically have a small(er) coefficient of thermal expansion (CTE), and a derivative dn_T/dT of the refractive index relative to temperature T. Indeed, in some instances, a ratio of the derivative dn_T/dT of the refractive index relative to temperature T may even be positive.

Design Considerations for a Multi-Element Component

As discussed further below, design considerations for an optical component with multiple elements (i.e., “multi-element”) may include focus power ϕ, athermalization and achromatism. In some examples, focus power in a multi-element optical component (e.g., a multi-element lens) may be calculated as follows:

φ=∑ik φi, and φ=φF-φC=∑ikφiVi=0.

Furthermore, a ratio of focal shift to a change in temperature in a multi-element optical component may be calculated as follows:

Δ⁢fΔ⁢T=-(1φ)2⁢∑1kγi⁢φi=αh⁢L0.

In some examples, α_h may be a coefficient of thermal expansion (CTE) for a lens barrel, L₀ may be a barrel length and V_i may be an Abbe number of the material selected. Also, in some examples, an Abbe number may indicate a dispersion of an optical material, wherein a high(er) Abbe number value may indicate a lower dispersion.

In some examples, a doublet may provide greater thermal stability. For example, as discussed further below, in some examples, a plastic and glass (i.e., mixed material) doublet may be designed to achieve athermalization.

Design Considerations Associated with an “Attached” Multi-Element Component

In some examples, a multi-element component may be “attached” in that two or more of the multiple elements may be physically attached to each other. One example of an attached multi-element component may be a doublet. In some examples, a doublet may be a type of lens made up of two simple lenses paired together.

FIG. 4 provides an illustration of a doublet 400. In a doublet configuration, design requirements of focus power, achromatic and athermalization may be calculated. In some examples, focus power and a focal shift in a doublet may be calculated as follows:

φ=φ1+φ2, and Δ⁢fF⁢C=(1φ)2⁢(φ1V1+φ1V2)=0.

Furthermore, a ratio of focal shift to a change in temperature in a multi-element optical component may be calculated as follows:

Δ⁢fΔ⁢T=-(1φ)2⁢(γ1⁢φ1+γ2⁢φ2)=αh⁢L0.

FIG. 5 illustrates focal shift results 500 from a plastic doublet versus focal shift results for a plastic singlet. In this instance, both the plastic doublet and the plastic singlet had specifications as shown in FIG. 2.

In some examples, it may be observed that a focal shift of plastic doublet may be smaller at −25° C. (e.g., 4 micron (4 μm) smaller) and smaller at 85° C. (e.g., 5.0 micron (5 μm) smaller) than that of a plastic singlet having similar characteristics. In some instances, this may be because as temperature may rise, a focal length decrease of a first element may cancel a focal length increase of a second element. Accordingly, in some examples, a “total” shift of a plastic doublet may be smaller than that of a plastic singlet.

Nevertheless, it should be appreciated that since thermal characteristics of materials of the plastic doublet may be similar, athermalization characteristics may remain unsatisfactory. Indeed, in some instances, a plastic doublet may not meet athermalization design requirements because there may limited options of plastic materials that may be utilized, and thermal characteristics of these options may be too similar. On the other hand and as discussed further below, it may also be observed that a doublet lens with one or more plastic elements combined with and one or more glass elements may satisfy an athermalization requirement over a particular temperature range.

Design Consideration Associated with a “Separated” Multi-Element Optical Component

In some examples, for a separated multi-element optical component, an initial design requirement may be calculated as follows:

φ=1f=φ1+h2h1⁢φ2+h3h1⁢φ3+…+hkh1⁢φk=∑iihih1⁢φi.

In some examples, effective power of each element included in a separated multi-element optical component may be calculated as follows:

φi′=hih1⁢φi.

Also, in some examples, an Abbe number and a coefficient of thermal expansion (CTE) of each element included in a separated multi-element optical component may be calculated as follows:

Vi′=h1hi⁢Vi, and γi′=hih1⁢γi.

Furthermore, for a separated multi-element optical component, to meet the requirements of the focus power ϕ, athermalization and achromatism, design requirements may be provided as follows:

φ=∑ikφi′=∑ikhih1⁢φi, Δ⁢fΔ⁢T=-(1φ)2∑1kγi′⁢φi′=-(1φ)2∑ik(hih⁢1)2⁢γi⁢φi=αh⁢L0, and φ=φF-φC=∑ikφi′Vi′=∑ik(hih⁢1)2⁢φiVi=0.

Reference is now made to FIGS. 6A-B. FIG. 6A illustrates a block diagram of a system environment, including a system, that may be implemented to design optical components, including multi-element optical components, that may provide passive athermalization and aberration correction over an entire field of view (FOV). FIG. 6B illustrates a block diagram of the system that may be implemented to design optical components, including multi-element optical components, that may provide passive athermalization and aberration correction over an entire field of view (FOV).

As will be described in the examples below, one or more of system 600, external system 610 and system environment 6000 shown in FIGS. 6A-B may be operated by a service provider to fabricate and/or implement an optical device. It should be appreciated that one or more of the system 600, the external system 610 and the system environment 6000 depicted in FIGS. 6A-B may be provided as examples.

While the servers, systems, subsystems, and/or other computing devices shown in FIGS. 6A-B may be shown as single components or elements, it should be appreciated that one of ordinary skill in the art would recognize that these single components or elements may represent multiple components or elements, and that these components or elements may be connected via one or more networks. The middleware may include software hosted by one or more servers.

In some examples, the external system 610 may include any number of servers, hosts, systems, and/or databases that store data to be accessed by the system 600 and/or other network elements (not shown) in the system environment 6000. In addition, in some examples, the servers, hosts, systems, and/or databases of the external system 610 may include one or more storage mediums storing any data.

The system environment 6000 may also include the network 620. In operation, one or more of the system 600 and the external system 610 may communicate with one or more of the other devices via the network 620. The network 620 may be a local area network (LAN), a wide area network (WAN), the Internet, a cellular network, a cable network, a satellite network, or other network that facilitates communication.

It should be appreciated that in some examples, and as will be discussed further below, the system 600 may be configured to utilize various techniques and mechanisms to design optical components, including multi-element optical components, that provide may passive athermalization and aberration correction over an entire field of view (FOV). Details of the system 600 and its operation within the system environment 6000 will be described in more detail below.

As shown in FIGS. 6A-B, the system 600 may include processor 601 and the memory 602. In some examples, the processor 601 may be configured to execute the machine-readable instructions stored in the memory 602. It should be appreciated that the processor 601 may be a semiconductor-based microprocessor, a central processing unit (CPU), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), and/or other suitable hardware device.

In some examples, the memory 602 may have stored thereon machine-readable instructions (which may also be termed computer-readable instructions) that the processor 601 may execute. The memory 602 may be an electronic, magnetic, optical, or other physical storage device that contains or stores executable instructions. The memory 602 may be, for example, Random Access memory (RAM), an Electrically Erasable Programmable Read-Only Memory (EEPROM), a storage device, an optical disc, or the like.

The memory 602, which may also be referred to as a computer-readable storage medium, may be a non-transitory machine-readable storage medium, where the term “non-transitory” does not encompass transitory propagating signals. It should be appreciated that the memory 602 depicted in FIGS. 6A-B may be provided as an example. Thus, the memory 602 may or may not include additional features, and some of the features described herein may be removed and/or modified without departing from the scope of the memory 602 outlined herein. It should be appreciated that, and as described further below, the processing performed via the instructions on the memory 602 may or may not be performed, in part or in total, with the aid of other information and data.

As used herein, an “optical component” may include any device or component that may be utilized to manipulate (e.g., focus, disperse, etc.) a light beam. In some examples, the optical component may include an arrangement of one or more lenses. In one example, the optical component may be included and utilized in an optical device, such as an virtual reality (VR) headset.

In some examples, and as discussed further below, the optical component may include one or more elements. That is, as used herein, an “element” or “optical element” may include any item that may be included in a optical component. In one example, the optical element may consist of a single lens element that may be one of a plurality of lens elements to be included in a lens component.

Also, as used herein, an “optical element configuration” may include an arrangement or setting of one or more optical elements. So, in one example, a plurality of optical elements (e.g., lens elements) may be selected or arranged to comprise an optical component. As discussed further below, in some examples, an optical element configuration may be selected and/or arranged with respect to one or more requirement(s), such as an athermalization requirement and/or an achromatism requirement.

In some examples, the memory 602 may store instructions, which when executed by the processor 601, may cause the processor to: receive 603 design specifications for an optical component; enable 604 selection and/or generation of one or more optical elements to be included in an optical element configuration; enable 605 selection and/or generation of one or more optical element configurations; implement 606 an optimization function to optimize an optical element configuration; determine 607 if an optical element configuration may meet one or more initial specifications; enable 608 one or more adjustment(s) to an optical element configuration; and determine 609 if an optical element configuration may meet one or more additional specifications.

In some examples, the instructions 603 may receive design specifications for an optical component. In some examples, design specifications of an optical component that may be received via the instructions 603 may relate to F# or F/#, numerical aperture (NA), an operating spectrum and an on-axis field. As used herein, F/# may be a ratio of a lens focal length to a diameter of a pupil at entrance. In some instances, it may indicate an efficiency of photon collection of a lens. Also as used herein, numerical aperture (NA) may refer to a cone of light that may be made from a focusing lens. In some instances, numerical aperture (NA) may refer to a range of angles in which a lens can accept light and may therefore be defined as NA=n sin (α), where n refers to refractice index and α refers to lens collection angle. In other words, numerical aperture (NA) may describe a light-gathering capability of a lens, and in some examples, may indicate a range of angles at which a lens may accept light. In some examples, an operating spectrum may include a range of operating wavelengths. Furthermore, in some examples, an on-axis field may refer to a centered field of view. It should be appreciated that, in some examples, the design specifications may include design restrictions.

In some examples, the instructions 604 may enable selection and/or generation of one or more optical elements. In some examples, and as discussed further below, the one or more optical elements may be included in an optical element configuration. In particular, the instructions 604 may enable selection of a material for each of one or more optical elements to be included in the optical element configuration. FIG. 7 illustrates a table including various materials that may be used in fabrication of a multi-element optical component. In some examples, the instructions 604 may select a plastic material (e.g., EP5000, EP7000, etc.) or a glass material (e.g., MP-FCD500-20, L-LAL15, etc.). In some examples, the instructions 604 may select the material based on one or more associated specifications. FIG. 8 illustrates a table including specifications of various materials that may be used in fabrication/selection of one or more optical elements.

In some examples, the instructions 604 may select each of one or more optical elements with respect to an athermalization requirement. In particular, to assign a material to each of the one or more optical elements, the instructions 604 may enable selection of materials with particular thermal refractive coefficients. In some examples, the instructions 604 may enable selection of a small(er) absolute derivative dn_T/dT of the refractive index relative to temperature T for a positive element (i.e., an optical element that may product converging light) and large(r) derivative dn_T/dT of the refractive index relative to temperature T for a negative element (i.e., an optical element that may produce diverging light). Also, in some examples, for axial color correction, the instructions 604 may enable selection of a large Abbe number material for a positive element and a negative element.

In some examples, the instructions 605 may enable generation a one or more optical element configurations. In some examples, the instructions 605 may utilize one or more optical elements (e.g., as selected and/or generated via the instructions 604) to populate one or more optical element configurations. Also, in some examples, the instructions 605 may also enable the one or more optical elements to be selected with respect to an athermalization requirement. It should be appreciated that, in some examples, a first optical element and a second optical element of the one or more optical elements in an optical element configuration may be arranged to be attached (as discussed above), while in other examples, the first optical element and the second optical element of the one or more optical elements in the optical element configuration may be arranged to be separated (as discussed above).

Furthermore, in some examples, the instructions 605 may enable testing of one or more optical elements of an optical element configuration with respect to a plurality of temperature settings. In some examples, the plurality of temperature settings may reflect a temperature range that an optical component may be subject to during operation. In one example, the plurality of temperature settings may include 0 degrees (0°), 35 degree (35°) and 65 degrees (65°) Fahrenheit. FIG. 9A illustrates graph of focus shift versus optical transfer function for a multi-element optical component at 0 degrees (0°). FIG. 9B illustrates graph of focus shift versus optical transfer function for a multi-element optical component at 35 degrees (35°). FIG. 9C illustrates a graph of focus shift versus optical transfer function for a multi-element optical component at 65 degrees (65°).

In some examples, the instructions 606 may implement an optimization function to optimize an optical element configuration. As used herein, an “optimization function” may include any function that may be implemented to select one or more optical elements for inclusion in an optical element configuration.

So, in some examples, the instructions 606 may implement an optimization function meet one or more athermalization requirement(s). So, in some examples, implementation of the optimization function may include selection of a focal length radius for each element. Furthermore, in some examples, the instructions 606 may implement an optimization function to compute optical power φ_ki, a marginal ray height h_ki and a thermal refractive power γ_i for each element to meet one or more athermalization requirement(s). Also, in some examples, the instructions 606 may implement an optimization function with respect to an effective focal length (EFFL) of an optical component. It should be appreciated that, in some examples, an optimization function may enable optimization of each optical element in an optical element configuration in order to meet one or more athermalization requirement(s). In some examples, an optimization function may also be implemented to require each optical element in an optical element configuration to meet an achromatism requirement. In one example, the achromatism requirement may be calculated as:

Δf_FC=0