CX-0693
`
`D2
`
`Illumination
`
`Tungsten and Sunlight
`
`
`This page and those that follow show typical spectra of
`several common illumination sources.
`
`Tungsten Lamp (CIE A)
`
`350
`
`400
`
`450
`
`500
`
`550
`
`600
`
`650
`
`700
`
`750
`
`wavelength (nm)
`
`Sunlight (CIE D65)
`
`350
`
`400
`
`450
`
`600
`550
`500
`wavelength (nm)
`
`650
`
`700
`
`750
`
`
`
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`CX-0693
`
`Sources for Illumination
`
`Ze
`
`Fluorescent Lamps
`
`
`Warm White Fluorescent
`
`350
`
`400
`
`450
`
`600
`550
`500
`wavelength (nm)
`
`650
`
`700
`
`750
`
`
`Daylight Fluorescent
`
`q
`
`I
`
`q
`
`I
`
`I
`
`q
`
`350
`
`400
`
`450
`
`500
`
`550
`
`600
`
`650
`
`700
`
`/750
`
`wavelength (nm)
`
`
`
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`

`CX-0693
`
`24
`
`Illumination
`
`H.P. Sodium and Metal Halide
`
`
`350
`
`400
`
`450
`
`500
`
`550
`
`600
`
`650
`
`700
`
`750
`
`High Pressure Sodiumwah.
`Metal Halidesll
`
`wavelength (nm)
`
`350
`
`400
`
`450
`
`500
`550
`600
`wavelength (nm)
`
`650
`
`700
`
`750
`
`
`
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`

`CX-0693
`
`Sources for Illumination
`
`25
`
`Xenon and White LEDs
`
`
`Xenon
`
`350
`
`400
`
`450
`
`500
`
`550
`
`600
`
`650
`
`700
`
`750
`
`wavelength (nm)
`
`White Light LED (Blue + YAG)
`
`350
`
`400
`
`450
`
`500
`
`550
`
`600
`
`650
`
`700
`
`750
`
`wavelength (nm)
`
`
`
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`

`CX-0693
`
`26
`
`Illumination
`
`Light Emitting Diodes (LEDs)
`
`
`LEDs are moderately narrowband emitters with an
`approximately Gaussian spectral shape. The spectrum of
`an LED is often expressed by a single wavelength, with
`four different single-wavelength descriptions in general
`use. The most common spectrum-based description is the
`peak wavelength, A», which is the wavelength of the
`peak of the spectral density curve. Less commonis the
`center wavelength, Aosm, which is
`the wavelength
`halfway between the two points with a spectral density of
`50% of the peak. For a symmetrical spectrum, the peak
`and center wavelengths are identical. However, many
`LEDs have slightly asymmetrical spectra. Least common
`is the centroid wavelength, A-:, which is the mean
`wavelength. The peak, center, and centroid wavelengths
`are all derived from a plot of S,(A) versus A. The fourth
`description,
`the dominant wavelength,
`du,
`is
`a
`colorimetric quantity that is described in the section on
`color. It
`is the most
`important description in visual
`illumination systems because it describes the perceived
`color of the LED.
`
`Spatially, LEDs, especially those in lens-end packages,
`are often described by their viewing angle, which is the
`full angle between points at 50% of the peak intensity.
`
`LEDs
`
`ef
`
`350
`
`400
`
`450
`
`500
`
`550
`
`600
`
`650
`
`700
`
`750
`
`wavelength (nm)
`
`
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`

`

`CX-0693
`
`Illumination Properties of Materials
`
`27
`
`Transmittance, Reflectance, and Absorptance
`
`
`Several alternative methods describe the response of
`materials to illumination. One common approach is the
`ratio of
`the light
`that
`is
`transmitted,
`reflected, or
`absorbed to the incident light. This method describes a
`material by its transmittance, 1, its reflectance, p, or
`its absorptance, a. Do not confuse absorptance with
`absorbance, A, which is equivalent to optical density
`(OD) and is a conversion of transmittance or reflectance
`to a log scale. For example, 10% transmittance can be
`described as 1A, 1% as 2A,ete.
`
`
`
`
`
`Transmittance = B/A
`Reflectance = C/A
`Absorptance = (A-B-C)/A
`
`Transmitted
`light, B
`
`Incidentlight, A
`
`Reflected
`light, C
`
`A material that produces intensity proportional to the
`cosine of the angle with the surface normal
`is called
`Lambertian. The radiance of a Lambertian surface is
`constant with viewing direction (since the projected area
`of a viewed surface is also proportional to the cosine of the
`angle with the
`surface normal). Furthermore,
`the
`directional distribution of scattered light is independent
`of the directional distribution of the incident illumination.
`It
`is impossible to tell, by looking at a Lambertian
`surface, where the incident light comes from. Perfectly
`Lambertian surfaces
`don’t
`really exist, but many
`materials,
`such as matte
`paper,
`flat paint,
`and
`sandblasted metal (in reflection), as well as opal glass and
`sandblasted
`quartz
`in transmission),
`are
`good
`Lambertian approximations
`over
`a wide
`range
`of
`incidence and view angles.
`
`
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`

`CX-0693
`
`28
`
`Illumination
`
`Reflectance Factor and BRDF
`
`
`A quantity sometimes confused with reflectance is the
`reflectance factor, R. The reflectance factor is defined
`in terms of a hypothetical perfectly reflecting diffuser
`(PRD), a surface that is perfectly Lambertian and has a
`100% reflectance. The reflectance factor is the ratio of the
`amountof light reflected from the material to the amount
`of light that would be reflected from a PRD if similarly
`illuminated and similarly viewed.
`
`A i
`Lambertian
`
`100% reflectance
`
`Notes on reflectance (p) and the reflectance factor (R):
`e Fora Lambertian surface, p and R are identical.
`e Reflectance must be between O
`and 1. The
`reflectance factor is not similarly bound. A highly
`polished mirror, for example, has near-zero R for any
`nonspecular incident and viewing angles, and a very
`high R (~1.0) for any specular incident and viewing
`angles.
`The reflectance factor is more closely related to the
`bidirectional reflectance distribution function
`(BRDF)than to reflectance. The BRDF is defined as
`the radiance of a surface divided by its irradiance:
`
`e
`
`BRDF = L/E.
`
`e
`
`reflectance factor measures per hemisphere
`The
`(there are m projected steradians in a hemisphere)
`what the BRDF measuresper projected steradian:
`
`R= BRDFn.
`
`
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`

`CX-0693
`
`Illumination Properties of Materials
`
`29
`
`Harvey / ABg Method
`
`
`The Harvey or ABg method is used to parameterize
`scatter from a weakly scattering surface, which is typical
`for optical surfaces such as lenses and mirrors. It also can
`be used to model Lambertian surfaces and anisotropic
`(i.e., asymmetric) scatter. An example for a three-axis
`polished surface is provided here, which has a total
`integrated scatter (TIS or TS) of about 1.6%. The
`vertical scale represents the BSDF,
`for which an R
`(reflection) or TJ (transmission) can be substituted for the
`S (surface). The horizontal scale represents the absolute
`difference between Bo = sino, or the specular direction,
`and B = sin®@, or any direction away from specular. Note
`that both axes are plotted in log space such that the roll-
`off slope is linear. The ABg parameters are:
`g is the slope of the roll-off as shown in the figure
`whose value of 0 defines a Lambertian surface.
`B is theroll-off parameter defined as
`
`B-
`
`
`
`Brolloff
`
`8
`
`
`
`A is the amplitude factor and can be found from
`
`A
`BSDF =—— —___.,
`B+|B-8,|
`
`Integrated scatter:
`
`Rolloff point:
`Beta:
`0.00773
`BSDF: 45.5
`
`ABg:
`A: 3.14e-006
`B: 6.89e-008
`g: 3.39
`
`0.01596
`
`— Data
`— Signature
`—— Synthetic
`
`Josccccccves|
`
`:
`i
`te005
`fonotret
`3
`i
`i
`i
`HE-005 |aie oof
`
`Fi
`
`:
`i
`0.0
`
`
`
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`

`

`CX-0693
`
`30
`
`Illumination
`
`Directional Properties of Materials
`
`
`e
`
`e
`
`e
`
`The reflectance of a material can depend on the direction
`of the incident light. This dependenceis often indicated by
`a number or letter.
`e
`(0°): reflectance for normal incidence.
`e
`(45°): reflectance for a 45-deg oblique incidence.
`e
`(d) or p(h): reflectance for diffuse illumination.
`The reflectance factor of a material can depend on both
`the direction of illumination and the viewing geometry.
`This is usually indicated by two letters or numbers, the
`first indicating the incident geometry and the second the
`viewing geometry.
`e
`R(0°/45°): the reflectance factor for normal incidence
`and a 45-deg oblique viewing (a common geometry for
`measuring the color of a surface).
`incidence
`R(0°/d):
`the reflectance factor for normal
`and diffuse (everything except the specular) viewing
`only.
`near-normal
`for
`factor
`reflectance
`the
`R(8%/h):
`incidence and hemispherical
`(everything,
`including
`the specular) viewing.
`R(45°vh): the reflectance factor for hemispherical illu-
`mination and a 45-deg oblique viewing.
`
`
`
`The same notation used for reflecting materials can
`be applied to transmitting materials, where trans-
`mittance t can be dependent on incident geometry,
`and the transmittance factor, 7, on both the incident
`and transmitting geometries. The use of
`the
`transmittance
`factor
`is
`not
`as
`common
`as
`transmittance,
`reflectance,
`and the
`reflectance
`factor.
`
`Some materials have reflecting properties that are not the
`same for every azimuthal angle, even for
`the same
`elevation angle, e.g., the specular geometry of mirrorlike
`surfaces has vastly different reflecting properties than
`any geometry with the same incident and reflecting
`elevation angles that are not both in the same plane with
`the surface normal.
`
`
`
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`
`

`

`CX-0693
`
`Illumination Properties of Materials
`
`31
`
`Retroreflectors—Geometry
`
`Retroreflectors reflect incident light back toward the
`direction of the light source, operating over a wide range
`of angles of incidence. Typically they are constructed in
`one of two different forms, 90-deg corner cubes or high
`index-of-refraction transparent spheres with a reflective
`backing. Retroreflectors
`are used in transportation
`systems as unlighted night-time roadway and waterway
`markers,
`as well as
`in numerous optical
`systems,
`including lunar ranging. Some are made of relatively
`inexpensive plastic pieces or flexible plastic sheeting, and
`some are madeof high-priced precision optics.
`
`The performance of retroreflectors is characterized within
`a geometrical coordinate system, usually with three
`angles for the incident and viewing geometries and a
`fourth orientation angle for prismatic designs like corner
`cubes, which are not
`rotationally isotropic in their
`performance. All the geometric variations are described in
`detail in ASTM E808-01, Standard Practice for Describing
`Retroreflection, along with expressions for converting from
`one geometric system to another.
`
`Two angles commonly used to specify the performance of
`retroreflectors are the entrance angle,
`6, and the
`observation angle, a. The entrance angle is the angle
`between the illumination direction and the normal to the
`retroreflector surface. High-quality retroreflectors work
`over fairly wide entrance angles, up to 45-deg or more (up
`to 90 deg for pavement marking). The observation angle,
`the angle between the illumination direction and the
`viewing direction,
`is generally very small, often one
`degreeorless.
`
`Another useful angle for interpreting the performance of
`retroreflectors is the viewing angle,v, the angle between
`the viewing direction and the normal to the retroreflector
`surface.
`
`
`
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`

`CX-0693
`
`32
`
`Illumination
`
`Retroreflectors—Radiometry
`
`
`The performance of retroreflectors is quantified by several
`coefficients. These are the most common:
`
`Ri, coefficient of retroreflected luminousintensity,
`
`I
`R,=—,
`E.
`where £, is the illuminance on a plane normal to the
`direction of illumination, and J is the intensity of the
`illuminated retroreflector.
`
`Ra, coefficient of retroreflection,
`p, fi HA,
`AE.
`where A is the area of the retroreflector.
`
`Rx, coefficient of retroreflected luminance,
`Hy de
`
`cosv.
`££,
`the luminance in the direction of
`
`L
`
`the ratio of
`is
`observation to F.
`
`Ro, coefficient of retroreflected luminous flux:
`_ fy
`
`° cosB.
`Rr, retroreflectance factor
`wef, wel,
`_
`n-R,
`
`7 A-cosB-cosv 7 cosB-cosv 7 cosB
`
`BF
`
`It is the retroreflectance factor, Rr that is numerically
`equivalent to the reflectance factor, R.
`
`Retroreflectors are often specified by the coefficient of
`retroreflection, Aa,
`for various observation angles and
`entrance angles.
`
`Values for Ra of several hundred (cd/m?)/lux are not
`uncommon, corresponding to reflectance factors up to and
`over 1000.
`
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`

`CX-0693
`
`Illumination Transfer
`
`33
`
`Lambertian and Isotropic Models
`
`
`There are no direct “conversion factors” between the four
`basic quantities in illumination: flux, ©; irradiance, E;
`intensity, I; and radiance, L. But for many situations,
`knowledge of one factor allows the calculation of the
`others. Making
`this
`calculation
`usually
`requires
`knowledge of the directional properties of the illuminating
`source, or at
`least a fair model of these directional
`properties. The two most common models are isotropic
`and Lambertian.
`
`An isotropic source is defined here as having intensity
`independentof direction. For a Lambertian source, the
`radiance is independent of direction and the intensity is
`therefore proportional to the cosine of the angle with the
`surface normal. A few nearly isotropic sources exist, such
`as a round, frosted light bulb, a frosted ball-end on a fiber,
`andaline filament (in one plane, anyway). However, most
`flat radiators, diffusely reflecting surfaces, and exit pupils
`
`of are more_nearlyilluminating optical systems
`
`
`
`Lambertian than isotropic. Reasonable predictions can be
`made by modeling them as Lambertian.
`
`The modelof directional illumination properties need only
`apply, of course, over the range of angles applicable to
`your particular situation. In many cases,
`the mutually
`contradictory models of an isotropic and a Lambertian
`source are used simultaneously. This is valid over small
`angular ranges where the cosine of the angle with the
`surface normal doesn’t change much. This assumption is
`not all
`that
`restricting. For example,
`for a
`small
`Lambertian source illuminating an on-axis circular area,
`the error in flux caused by using an isotropic modelis less
`than 1% for a subtended full angle of 22 deg [NA = 0.19,
`//2.6], less than 5% for a full angle of 50 deg [NA = 0.42,
`#/1.2], and less than 10% for 70 deg [NA = 0.57, £/0.9].
`However, for a full angle of 180 deg (a full hemisphere),
`the error is 100%!
`
`
`
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`
`

`

`CX-0693
`
`34
`
`Illumination
`
`Known Intensity
`
`
`Consider a small source at a distance. For a known
`intensity that is essentially constant over all relevant
`directions, 1.e., toward the illuminated area:
`
`
`
`where J is the intensity of the radiating area in the
`direction of the illuminated area;
`Ar is the radiating area;
`8 is the angle between the normal to the radiating area
`and the direction of illumination;
`Ar cos® is the projected radiating area as viewed from the
`illuminated area;
`Aj is the illuminated area;
`E (x1) is the angle between the normal to the illuminated
`area and the direction of illumination (assumed
`constant over this small angular range);
`d is the distance between the two areas (assumed to be
`constant);
`is the solid angle formed by the illuminated area when
`viewed from the radiating area (assumed to be small);
`cosis the corresponding projected solid angle (for
`small solid angles);
`Eis the irradiance at the illuminated area;
`Qj is the total flux irradiating the illuminated area; and
`Lis the radiance of the radiating area.
`
`Q =
`
`, M
`
`PAGE 48 OF 154
`
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`
`E
`
`7p
`
`A, cos®
`
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`
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`

`CX-0693
`
`Illumination Transfer
`
`35
`
`Known Flux and Known Radiance
`
`
`If, in the samesituation, the flux within the solid angle
`is known, then the intensity is
`I=9,/o,
`
`the irradiance is
`
`and the radianceis
`
`E=@,/A,,
`
`om eae ter
`
`
`
`Consider the same situation, but not necessarily with a
`small radiating area or small illuminated area:
`
`L
`
`0,Q
`
`
`
`If the radiance is known andthe radiating area is small,
`then
`
`I=LA, cosé.
`
`If cos® is essentially constant from all points on the
`radiating area to all points on the illuminated area, then
`®.=LA,@cos®=LA,Q.
`
`If cos@ varies substantially over the illuminated area,
`then the second form of this equation, using the projected
`solid angle, should be used.
`Since there are x projected steradians in a hemisphere,
`the total flux radiated (for a Lambertian radiator) is
`®. =LA, 7.
`
`E=
`
`The irradiance at the illuminated area (£) is
`®, LA,Q LA, cos@cos€é
`
`A, A,
`d’
`where Qis the projected solid angle of the radiating area
`when viewed from the illuminated spot.
`
`=L Q,,
`
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`

`CX-0693
`
`36
`
`Illumination
`
`Form Factor and Average Projected Solid Angle
`
`
`Here the approximations of constant cosines cannot be
`used.
`
`
`
`The angles between
`the normal
`to the
`radiating
`surface
`and the directions
`to points on the
`illuminating—sur-
`face vary not only with the locations of the points on the
`illuminated surface, but also with the locations of points
`on the radiating surface. The concept of projected solid
`angle takes the former into account, but not the latter.
`What is needed is an average projected solid angle,
`Q toi, which is the projected solid angle subtended by the
`illuminated area and averaged over all points on the
`radiating area. Then the illuminating flux, @;, from a
`Lambertian radiator is
`
`0, =LA, Dyog = °. Q
`
`
`
`T
`
`rtot*
`
`In practice, the average projected solid angle is not used.
`However,
`its geometrical equivalent, called the form
`factor, Fatos,
`is used. The only difference between the
`form factor and the average projected solid angle is a
`multiplier of x:
`
`Fsob = Out®
`the
`The form factor measures in hemispheres what
`
`average projected solid angle measures in_projected
`steradians. The form factor also can be interpreted as the
`portion of the flux leaving a Lambertian radiator, a, that
`illuminates a surface, b:
`©,.=-0 Frtoi*
`Note that the form factor is directional, as are the solid
`and the projected solid angles. Fa w »
`is not in general
`equal to F» toa. However, the product of the area and the
`form factor is constant:
`A, FFatob =A, F, toa*
`
`
`
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`

`

`CX-0693
`
`Illumination Transfer
`
`37
`
`Configuration Factor
`
`
`The form factor and the average projected solid
`angle both link two extended areas. The form factor
`measures in hemispheres what
`the average projected
`solid angle measures in projected steradians. Another
`term, the configuration factor, C, is similarly related to
`the projected solid angle, linking a small area with an
`extended area. Like the form factor,
`the configuration
`factor measures in hemispheres what the projected solid
`angle measures in projected steradians:
`
`C=Q/n.
`
`for
`Tables of configuration factors and form factors
`myriad geometries
`can be
`found in handbooks on
`illumination, in books on radiative heat transfer (where
`the issues are identical to illumination by Lambertian
`radiators),
`and on the Internet. Three
`cases with
`applicability to many optical situations are listed here:
`
`Case 1: Small area to an extended circular area; both
`areas parallel and with axial symmetry.
`
`radius, r
`
`C=
`
`and
`
`
`
`go a 2
`
`= sin’ 0
`
`Zz
`Tr
`=—— = asin’ 6.
`r +d
`
`
`
`PAGE 51 OF 154
`
`MASITC_01080431
`
`MASIMO 2054
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`CX-0693
`
`38
`
`Illumination
`
`Useful Configuration Factor
`
`
`Case 2: Small area to an extended circular area; both
`areas parallel, but without axial symmetry.
`
`
`
`or, equivalently:
`
`1
`
`1+tan® 6-—tan’ 0
`|tan‘ o+ (2tan’ 8)(1 —tan” 8) + sec! 6| =
`
`and
`
`O= nC,
`
`These expressions degenerate to the expressions for case 1
`above when x, or equivalently, 6, is equal to zero.
`
`
`
`MASITC_01080432 MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`PAGE 52 OF 154
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`
`

`

` radius, /;
`
`area, A,
`
`area, A;
`
`CX-0693
`
`Illumination Transfer
`
`og
`
`Useful Form Factor
`
`
`Case 3: An extended circular area illuminating another
`extended circular area; both areas parallel and centered
`on the sameaxis.
`
`
`
` radiating__illuminated
`
`Pr.
`Pr.
`F
`z
`2
`1+(4)
`1+(4)
`1
`Fn [—_ Ss ||3| a5
`e)
`2
`r.
`
`1
`
`Some numerical values of F; oi for this case are shown in
`the table below for
`several
`sizes of
`radiating and
`illuminated disks (each expressed as a multiple of the
`distance between the two parallel circular areas that are
`centered on the sameaxis).
`
`Form Factor,F r toi
`
`rild
`
`0.03
`
`0.10
`
`0.30
`
`1.00
`
`38.00
`
`10.0
`
`0.03
`
`.001
`
`.010
`
`.083
`
`.500
`
`.900
`
`.990
`
`0.10
`
`.001
`
`.010
`
`.082
`
`.499
`
`.900
`
`.990
`
`0.30
`
`.001
`
`.009
`
`.077
`
`.489
`
`.899
`
`.990
`
`1.00
`
`.000
`
`.005
`
`.044
`
`.382
`
`.890
`
`.990
`
`rrid
`
`3.00
`
`.000
`
`.001
`
`.009
`
`.099
`
`.718
`
`.989
`
`10.0
`
`.000
`
`.000
`
`.001
`
`.010
`
`.089
`
`.905
`
`
`
`PAGE 53 OF 154
`
`MASITC_01080433
`
`MASIMO2054
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`CX-0693
`
`40
`
`Illumination
`
`Irradiance from a Uniform Lambertian Disk
`
`
`as
`be modeled
`can
`illumination situations
`Many
`illumination by a uniform circular Lambertian disk,
`with the illuminated area parallel to the disk and at some
`distance from it.
`
`offset, x
`
`Radiating area
`
`Illuminated spot
`
`is equal to the
`The irradiance at the illuminated spot
`radiance of the radiating area times the projected solid
`angle of
`the radiating area when viewed from the
`illuminated spot:
`
`mH =0, De.
`If the illuminated spotis on axis (x = 0, 6= 0), then
`2
`E,=nL, sin’ 0=nrL, ——
`r'+d
`If the spot is offset from the axis, it is necessary to use the
`projected solid angle or the configuration factor discussed
`previously for case 2:
`
`1+tan* 5-—tan’* 6
`_t
`2 |tan’ 6+ (2tan’ 8)(1 —tan” 6) +sec* o\”
`
`form factor, and
`Note: The configuration factor,
`projected solid angle are useful mainly when the
`
`radiation pattern is Lambertian or nearly Lambertian.
`
`
`
`PAGE 54 OF 154
`
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`MASIMO 2054
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`Illumination Transfer
`
`4]
`
`Cosine Fourth and Increase Factor
`SSSCg.za7)!
`
`CX-0693
`
`Consider the previous case of illumination by a uniform
`circular Lambertian disk, with the illuminated area
`parallel to the disk and at some distance from it. For
`many values of aperture size (8) and field angle (6), the
`irradiance falls off very nearly at cos‘d, a phenomenon
`often referred to as the cosine-fourth law.
`
`Two of the cosine terms in the cos‘ law are due to the
`fact
`that, off axis,
`the distance increases with the
`cosine of 6 and the inverse square law applies. The
`third cosine factor comes from the Lambertian source,
`and the fourth from the fact
`that the illuminated
`
`surface is inclined to the direction of propagation.
`
`In reality, the cost “law’ is not exactly true, and is far
`from true for large values of 8 and 6. The table below
`displays values of the increase factor, F’, which is the
`multiplier
`that must be
`applied to the irradiance
`calculated by using the axial irradiance and cos? falloff. F’
`compensates for
`the inaccuracy in the “cosine-fourth”
`assumption:
`
`E,=n L, sin’ @-cos* 5: F”
`
`Increase Factor, F"
`
`Q
`
`(deg)
`
`18
`
`3.6
`
`7.2
`
`14.5
`
`30.0
`
`45.0
`
`NA
`
`0.03
`
`0.06
`
`0.13
`
`0.25
`
`0.50
`
`0.71
`
`fi#
`
`0
`
`10
`
`16
`
`8
`
`4
`
`2
`
`1
`
`0.71
`
`1.00
`
`1.00
`
`1.00
`
`1.00
`
`1.00
`
`1.00
`
`1.00
`
`1.00
`
`1.00
`
`1.01
`
`1.08
`
`1.05
`
`1.20
`1.11
`1.038
`1.01
`1.00
`1.00
`20
`d(deg)
`30
`1.00
`1.00
`1.01
`105
`1.23
`1.49
`
`40
`
`60
`
`100
`
`1.00
`
`1.02
`
`1.08
`
`1.37
`
`1.94
`
`1.00
`
`1.01
`
`1.02
`
`1.09
`
`1.48
`
`2.69
`
`The cost approximation is valid within a few percent up to
`very large apertures andfield angles.
`
`
`PAGE 55 OF 154
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`
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`IPR2022-01299
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`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`CX-0693
`
`42
`
`Illumination
`
`Known Irradiance
`
`
`
`If a surface is illuminated by a source of uniform intensity
`at a distance d and the irradiance on the surface is
`known, then the intensity of the source is
`
`Aj
`
`5
`
`E
`
`ee
`
`a.
`
`.
`2,
`
`
`i= sn ;
`cos&
`
`For any surface that is illuminated by
`uniform irradiance,
`the
`total
`flux
`illuminating the surface is
`
`@=E-A.
`
`The radiance of the surface, caused by the light reflecting
`from the surface, depends on the reflecting properties of
`the surface.
`
`If the surface is Lambertian over all angles of reflection
`(for this incident geometry), then
`
`-E
`p=P=,
`
`Tt
`
`wherepfis the reflectance of the surface for the relevant
`incident geometry.
`If the surface is not Lambertian over all angles but is
`Lambertian over the direction of concern, then
`i= ah
`,
`
`-E
`
`T
`
`where RF is the reflectance factor of the surface for the
`relevant
`incident geometry and for
`the direction of
`concern.
`
`
`PAGE 56 OF 154
`
`MASITC_01080436
`
`MASIMO 2054
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`CX-0693
`
`Illumination Transfer
`
`43
`
`a, Q, NA, and f/# for a Circular Cone
`
`
`The case of a circular disk subtending a knownhalf-angle,
`8, shows up often in illumination situations.
`
`There are at least four common ways of describing the
`cone:
`solid angle (@), projected solid angle (Q),
`numerical aperture (NA), and f-number (//#):
`
`w = 2n(1— cos 0)
`NA =n-sin@
`
`Q = msin’ 0
`f/# =1/2sin8,
`
`where n is the index of refraction.
`
`Cone subtended by a circular disk
`O(deg)
`@
`Q
`NA/n
`1.8
`0.003
`0.003
`0.03
`
`fi#
`16.00
`
`3.6
`
`7.2
`
`12.7
`
`14.5
`
`20.0
`
`25.0
`
`30.0
`
`35.0
`
`40.0
`
`45.0
`
`50.0
`
`60.0
`
`70.0
`
`80.0
`
`90.0
`
`0.012
`
`0.049
`
`0.154
`
`0.200
`
`0.379
`
`0.5389
`
`0.842
`
`1.14
`
`1.47
`
`1.84
`
`2.24
`
`3.14
`
`4.13
`
`5.19
`
`6.28
`
`0.012
`
`0.049
`
`0.152
`
`0.196
`
`0.367
`
`0.561
`
`0.785
`
`1.03
`
`1.30
`
`1.57
`
`1.84
`
`2.36
`
`2.77
`
`3.05
`
`3.14
`
`0.06
`
`0.13
`
`0.22
`
`0.25
`
`0.34
`
`0.42
`
`0.50
`
`0.57
`
`0.64
`
`0.71
`
`0.77
`
`0.87
`
`0.94
`
`0.98
`
`1.00
`
`38.00
`
`4.00
`
`2.27
`
`2.00
`
`1.46
`
`1.18
`
`1.00
`
`0.87
`
`0.78
`
`0.71
`
`0.65
`
`0.58
`
`0.53
`
`0.51
`
`0.50
`
`
`
`MASITC_01080437 MASIMO2054
`Apple v. Masimo
`IPR2022-01299
`
`PAGE 57 OF 154
`
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`Apple v. Masimo
`IPR2022-01299
`
`

`

`CX-0693
`
`44
`
`Illumination
`
`Invariance of Radiance
`
`
`Unlike intensity, which is associated with a specific point,
`and irradiance, which is associated with a specific surface,
`radiance is associated with the propagating light rays
`themselves. This distinction is not trivial and implies that
`the radiance of a surface can be considered separate from
`the actual physical emitter or reflector that produces the
`radiance.
`
`Consider a uniform Lambertian radiating source, A,, with
`radiance, L,, illuminating an area, Ai, through a limiting
`aperture that limits the solid angle of the source to o:
`
`Ey
`
`A
`
`The physical location of the radiating source is irrelevant.
`Only the solid angle matters. In fact, the physical location
`(and shape) can be assumed to be anywhere (and any
`shape) as long as the solid angle is the same. All of the
`following descriptions of the radiating area, Ai, A2, and As,
`are equivalent to A, from an illumination point of view:
`
`
`
`
`
`PAGE 58 OF 154
`
`MASITC_01080438
`
`MASIMO 2054
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`CX-0693
`
`Illumination in Imaging Systems
`
`45
`
`Image Radiance
`
`
`In an imaging system with no vignetting or significant
`aberrations,
`for Lambertian objects, point-by-point,
`the
`radiance of an imageis equalto the radiance of the object
`except
`for
`losses due to reflection, absorption, and
`scattering. These losses are usually combined into a
`single value of transmittance, t. This equivalence of
`radiance is true for virtual as well as real images, and for
`reflective or refractive imaging systems.
`
`Real Image
`
`Imaging
`System
`T
`
`Object
`L
`.
`Virtual Image
`
`.
`v
`
`eal
`Image
`L;= tLo
`
`
`
`Imaging
`System
`1
`
`Object
`L.
`
`A =
`
`;
`7
`Virtual
`Image
`L;= tLe
`
`Viewed from any point on a real image, the entire exit
`pupil of the optical system is also the radiance of the
`corresponding object point but reduced by T.
`
`Imaging
`System
`
`:
`v
`exit pupil = tLo
`exit pupil
`
`Object
`°
`
`
`
`MASITC_01080439 MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`PAGE 59 OF 154
`
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`

`

`CX-0693
`
`46
`
`Illumination
`
`Limitations on Equivalent Radiance
`
`
`the image radiance only exists when the
`In all cases,
`image is viewed through the exit pupil of the imaging
`system. When viewed in a direction that doesn’t include
`the pupil, the radiance is zero.
`|
`:
`3
`
`|
`
`i
`
`ae
`
`ow\ . L;= zero
`
`
`
`exit pupil
`
`
`
`then the angular
`is not Lambertian,
`If the object
`image
`is
`also not
`radiance of
`the
`distribution of
`Lambertian. The
`relationship between the
`angular
`
`distributions of object and image is_notradiances
`
`straightforward and must be determined by ray tracing
`on the specific system. However, in many practical cases,
`the entrance pupil of the imaging system subtends a
`small angle from the object, and the source is essentially
`Lambertian over this small angle.
`
`If the object and the image are in media of different
`refractive indices, mo for the object and ni for the image,
`then the expression for equivalent radiance is
`
`
`
`The point-by-point equivalence of radiance from object to
`image is only valid for well-corrected optical systems. For
`systems that suffer from aberrations or are not in focus,
`each small point in the object is mapped to a “blur spot” in
`the image. Thus, the radiance of any small spot in the
`image is related to the average of the radiances of the
`corresponding spot in the object and its surrounding area.
`
`
`
`PAGE 60 OF 154
`
`MASITC_01080440
`
`MASIMO 2054
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`Illumination in Imaging Systems
`
`47
`
`Image Irradiance
`aSSSSSSS
`
`CX-0693
`
`Since the exit pupil, when viewed from the image, has the
`radiance of the object, then the irradiance at the imageis
`the sameas the irradiance from a source of the same size
`as the exit pupil and the same radiance as the object
`(reduced by t). In most imaging systems, the exit pupil is
`round and the irradiance is the same as the irradiance
`from a uniform Lambertian disk:
`
` 8
`
`Exit pupil, L =t-L,
`
`Image
`
`E, =n tL, sin’ 0-cos*8- F’.
`
`A table of values for the increase factor, F', is presented
`in the section on illumination transfer. F' is very close to
`1.0 except for a combination of large field angle (6) and
`large aperture (9), which is not a common combination in
`imaging systems.
`
`The cos‘d term contributes to substantial field darkening
`in wide-angle imaging systems—for example, cos!45 deg =
`0.25.
`
`If the physical aperture stop is not the limiting aperture
`for all the rays converging to an off-axis image point, the
`light is vignetted. The irradiance at image points where
`there is vignetting will be lower than predicted.
`
`On axis, cos‘6 = 1.0 and # = 1.0. The imageirradiance on
`axis, Kio, is
`
`_
`“aa
`E,, =u tL, sin’ 0.
`
`
`
`PAGE 61 OF 154
`
`MASITC_01080441
`
`MASIMO 2054
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`CX-0693
`
`48
`
`Illumination
`
`fi#, Working f/#, T/#, NA, Q
`
`infinite conjugates (distant
`For a camera working at
`object, magnification,
`|m|<<1), the image irradiance can
`be expressed in terms of the lens’ f-number, //#:
`
`_ ai,
`ACA”
`
`is an “infinite
`This //#, usually associated with a lens,
`conjugates” quantity. When a lens is used at
`finite
`conjugates,
`the working f/-number, /f/#w, describes the
`cone angle illuminating the image:
`
`fit, = (Ft )-d—m),
`
`the image
`the lateral magnification of
`where m is
`(negative for real images), and the axial image irradiance
`is:
`
`— ath,
`A (fH)
`
`Note that fffw degenerates to the conventional “infinite
`conjugates”
`//# when the lens
`is used at
`infinite
`conjugates.
`Occasionally, a lens will be designated with a T-number,
`T/#, which combines the //# and the transmittance into a
`single quantity,
`T# =—— with axial image irradiance: E,, = th,
`#4
`Vt
`4 (T/#)
`
`Another descriptor of the image illumination cone angle is
`the numerical aperture, NA,
`
`NA = sin 0 with axial image irradiance: E,, = tL, NA’.
`
`In all cases, even without circular symmetry, on or off
`axis, the cone illuminating the image can be described by
`its projected solid angle, ©, with image irradiance:
`
`BE, =, Q.
`
`
`
`PAGE 62 OF 154
`
`MASITC_01080442
`
`MASIMO 2054
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2054
`Apple v. Masimo
`IPR2022-01299
`
`

`

`CX-0693
`
`Illumination in Imaging Systems
`
`49
`
`Flux and Etendue
`
`
`The total flux reaching the image is the product of the
`image irradiance and the area of the image. The image
`irradianceis proportional to the projected solid angle of
`the exit pupil when viewed fro