GB/T 4315.1-2009 PDF English
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Optical transfer function -- Part 1: Terminology and symbol
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GB/T 4315.1-2009: Optical transfer function -- Part 1: Terminology and symbol---This is an excerpt. Full copy of true-PDF in English version (including equations, symbols, images, flow-chart, tables, and figures etc.), auto-downloaded/delivered in 9 seconds, can be purchased online: https://www.ChineseStandard.net/PDF.aspx/GBT4315.1-2009
GB
NATIONAL STANDARD OF THE
PEOPLE’S REPUBLIC OF CHINA
ICS 37.020
N 30
Replacing GB/T 4315.1-1984
Optical transfer function - Part 1: Terminology and
symbol
(ISO 9334:2007, Optical transfer function - Definitions and mathematical
relations, MOD)
ISSUED ON: SEPTEMBER 30, 2009
IMPLEMENTED ON: DECEMBER 01, 2009
Issued by: General Administration of Quality Supervision, Inspection and
Quarantine of PRC;
Standardization Administration of PRC.
Table of Contents
Foreword ... 3
1 Scope ... 5
2 Normative references ... 5
3 Basic terms and definitions ... 5
4 Terms and definitions in measurement... 16
5 Symbol and unit name ... 21
Optical transfer function - Part 1: Terminology and
symbol
1 Scope
This part of GB/T 4315 specifies the terms, which are related to the optical
transfer function AND the mathematical relationship between them, based on
the relationship, BETWEEN the optical transfer function of the imaging system
AND the point spread function. It also specifies various important parameters,
which are needed to explain, in the measurement of the optical transfer function.
This part applies to the measurement of optical transfer function of all optical,
electro-optical, other imaging systems.
2 Normative references
The clauses in the following documents have become clauses of this part, by
reference to this part of GB/T 4315. For the dated references, the subsequent
amendments (excluding corrections) or revisions do not apply to this part;
however, parties who reach an agreement based on this part are encouraged
to study if the latest versions of these documents are applicable. For undated
references, the latest edition of the referenced document applies.
GB/T 4315.2 Optical transfer function - Part 2: Directives of measurement
(GB/T 4315.2-2009, ISO 9335:1995, Optical transfer function - Principles
and procedures of measurement, IDT)
3 Basic terms and definitions
3.1
Linearity
The characteristic of equalizing the response of an imaging system to the
input signal strength.
3.2
Linear range
The range of the input signal, within the display linearity of an imaging
PTF
The argument of the optical transfer function D (r, s).
Note: The phase transfer function is equal to zero, at zero spatial frequency. The
value of the phase transfer function is related to the position of the origin of the
reference coordinate system of the point spread function. The displacement of the
origin position will cause the phase transfer function to produce an additional term,
that is linear to r and s.
3.11
One-dimensional optical transfer function
D (r)
A one-dimensional representation of the OTF of a one-dimensional azimuth,
in a specified direction.
Note 1: In most cases, the transfer function is usually in one-dimensional form. At
this time, the spatial frequency variables, r and s, are simplified to a single spatial
frequency variable, r', and an orientation variable, Ψ, (see 4.21 and 4.22), where Ψ
is part of the imaging state (see Figure 1):
For convenience, D (r', Ψ) is written as D (r). By convention, the meridian OTF
corresponds to the meridian direction Ψ = 90°; the radial OTF corresponds to the
radial direction Ψ = 0°.
Note 2: Figure 1 respectively introduces the regional right-handed coordinate
system, (u, v) and (r, s), AND the right-handed pupil coordinate system. The
reference line of the azimuth angle Ψ is perpendicular to the constant irradiance
line of the image pattern. When scanning the slit or the edge of the blade, the
perpendicular direction is consistent with the scanning direction, THEN, the angle
Ψ is the included angle, BETWEEN the u axis or the r axis AND the scanning
direction.
If the starting point is the premise, a right-handed coordinate system must be used.
In optics, the meridian plane usually contains the x2-axis but not the x1-axis. The
specific descriptions are as follows:
a) The reference axis is the z-axis.
b) In the exit pupil's center, the exit pupil's coordinate system has its origin. The x-
axis is perpendicular to the meridian plane; the y-axis is located within the
meridian plane; the x, y, z form a right-handed coordinate system.
c) For the end point of the image vector h', the regional image field's coordinate
system (u, v) [or for the (r, s) of each Fourier invertible space] has its origin. The
u-axis (or r-axis) is perpendicular to the meridian plane; the v-axis (or s-axis)
lies within the meridian plane. For example, in the direction of the image vector
h', the reference axis's direction of a right-handed coordinate system is
composed by (u, v) or (r, s).
d) Calculate the azimuth angle Ψ, from the perpendicular direction of the reference
line's u-axis or r-axis to the image constant intensity line.
e) Calculate the reference angle Φ, from the reference mark vector of the
reference line to the meridian plane. When the mark is facing the opposite
direction of the reference axis, the mark that rotates counterclockwise is positive.
3.12
Spatial frequency
The reciprocal of the space distribution period of a straight-line sine.
Note: Spatial frequency is a variable in Fourier space. It can be expressed by a
straight line or an angle. The unit name of the spatial frequency is set as 1/mm or
1/milliradian (1/degree).
3.13
Line spread function
LSF
The naturalized irradiance distribution of the incoherent line source image,
which can be expressed as the convolution of the point spread function P (u,
v), wherein P (u, v) has an infinite narrow line whose length is contained in
the isoplanatic region δ (u). For a narrow line, which is parallel to the v-axis,
δ (u) is the Dirac delta function.
Where:
Imax - The maximum value of the amount of radiation emitted or irradiated;
Imin - The minimum value of the amount of radiation emitted or irradiated.
3.18
Modulation transfer factor
T (r0)
The MTF value under a certain spatial frequency r0.
Note: Under special circumstances, when the object is a sine grating of a certain
spatial frequency r0, meanwhile it is in the linear range and isoplanatic region, the
modulation transfer coefficient T (r0) is the ratio, of the modulation of the image to
the modulation of the object.
3.19
Phase transfer value
The PTF value under a certain spatial frequency r0.
Note: In the linear range and isoplanatic region, when a sinusoidal pattern's image
has a lateral displacement, as relative to the position of the geometrical optics
(Gaussian optics) image, the ratio of this displacement to the image period, which
is multiplied by 2π radians, to obtain the phase transfer value.
3.20
Wave aberration function
Wλ (x, y)
The optical path difference, BETWEEN the wavefront of the wavelength λ,
which is emitted by a given object point, on the exit pupil after passing
through the optical system, AND a reference sphere, which is centered on
the image point.
Note: The wavefront aberration function provides a measure of the phase change
of the wavefront through the exit pupil.
3.21
Pupil function
3.22
Amplitude point spread function
Amplitude impulse response
Ap, λ (u, v)
The relative distribution of the complex amplitude of point source image.
Note 1: After using an appropriate naturalization constant, the amplitude point's
spread function is the Fourier transform of the pupil function Pλ (x, y).
Where:
u, v - Cartesian coordinates, which use the geometric optical image point of the
object point as the origin, wherein the x-axis and the v-axis are respectively taken
to be parallel to x-axis and y-axis;
R - The reference spherical radius of the selected image point.
See Figure 1 and note 2 to 3.11.
Note 2: The relationship between the point spread function and the amplitude point
spread function is as follows:
Here the asterisk stands for complex conjugate.
3.23
Autocorrelation integral
Duffieux integral
The mathematical procedures, which are used to evaluate the
autocorrelation of the pupil function of monochromatic illumination, in this
part.
Note: Except where the imaging system has a particularly large aperture ratio or
field angle, the two-dimensional optical transfer function can be expressed as the
autocorrelation integral of the pupil function Pλ (x, y). According to the equation:
radiation, the spectral transmittance of the device, the spectral sensitivity of the filter
or detector.
Note 2: The weight function F (λ) must match the spectral characteristics of the
imaging equipment, which is related to the application.
4 Terms and definitions in measurement
4.1
Object pattern
The spatial distribution of radiation, that can be imaged by the test system.
4.2
Image pattern
Corresponding to the object pattern, the spatial distribution of radiation, that
can be detected at the output end of the imaging system.
4.3
Object field
The allowable range of the object pattern.
Note: The center of the object field and the center of the image field shall
correspond to each other.
4.4
Image field
The range of the detectable image pattern, which is formed by the system in
the test.
4.5
Analyzed area
The part of the image field, which is analyzed during OTF measurement.
4.6
Reference axis
A straight line, which is defined by an appropriate characteristic, that can be
Object (image) pattern vector
A vector pointing to the midpoint of the object (image) pattern (see Figure 1).
4.11
Reference mark vector
A vector, which is perpendicular to the reference axis AND pointing to a
reference mark of the specimen (see Figure 1).
4.12
Reference angle
The angle, BETWEEN the plane, which is formed by the reference mark
vector and the reference axis, AND the plane, which is formed by the pattern
vector and the reference axis.
Note: The coordinate system of the reference axis, which is defined in this way, is
a right-handed coordinate system, so the reference angle Ф is defined as shown in
Figure 1 (see Figure 1 and note 2 to 3.11).
4.13
Object field angle
The absolute value of the angle, BETWEEN the reference axis AND the
direction of radiation propagation, from the object at infinity object to the
entrance pupil of the test sample.
4.14
Image field angle
ω'
The absolute value of the angle, BETWEEN the reference axis AND the
direction of radiation propagation, from the exit pupil of the test sample to
the infinity image.
4.15
Object height
under test (such as mounting flanges or mounting special-purpose fixtures).
4.20
Reference plane
A plane of the reference surface.
4.21
Radial azimuth
The azimuth of the object pattern, when the direction of the slit, edge object
or grating line is the direction of the object or image pattern vector.
Note: Other azimuths are given by angle Ψ, as shown in Figure 1 and note 2 to
3.11.
4.22
Tangential azimuth
The azimuth of the object pattern, which is specified when the direction of
the slit, edge object or grating line is at right angles to the direction of the
object or image pattern vector.
Note 1: Other azimuths are given by angle Ψ, as shown in Figure 1.
Note 2: When the direction of the test pattern on the axis, slit, edge object or grating
line is toward the reference mark, it is set as the tangential azimuth. At this time,
the lens shall be installed, so that the reference mark is at the uppermost position.
4.23
Image scale
Magnification
The ratio of the image height to the object height, at the paraxial limit.
Note: In the case of infinite object and finite distance image conjugate, the image
scale is zero. When the object and the image are both infinitely conjugated, the
image scale is the angular magnification of the system. The angular magnification
is the ratio of tanω to tanω'.
4.24
Local image scale
......
Source: Above contents are excerpted from the full-copy PDF -- translated/reviewed by: www.ChineseStandard.net / Wayne Zheng et al.
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