Coherence scanning interferometry: linear theory of surface measurement
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JE E63, E65, F36, F47 JOURNAL OF ECONOMIC LITERATURE CLASSIFICATION NUMBER
- KW Exchange Rate Mechanism, Germany, rational expectations, transformation KEY WORDS AB ABSTRACT (Abstract follows.).
- In particular, unification was expected to give rise to an increase in German aggregate demand that would put upward pressure on output, inflation, and the exchange rate, and downward pressure on the current account balance in Germany.
- The model simulations also highlighted the contractionary effects of high German interest rates on other member countries of the Exchange Rate Mechanism of the European Monetary System.
- 1Gagnon is Senior Economist in the Division of International Finance, Board of Governors of the Federal Reserve System; Masson is Assistant Director in the Research Department, International Monetary Fund; and McKibbin is Professor of Economics at Australian National University and Nonresident Senior Fellow at the Brookings Institution.
- For the first time a socialist planned economy was being transformed into a capitalist market economy, and the transformation was occurring almost overnight.
II. An Overview of Developments Since Unification
- This section provides a capsule summary of the evolution of the main macroeconomic variables since economic unification in July 1990.
- Nevertheless, an overall picture emerges of a sharp fall in East German output, followed by a period of sustained growth that is faster than in the West.
- Investment is relatively strong in the East, but large fiscal transfers continue from West to East.
- Clearly, a first priority was to reduce the extent of state ownership and to convert the economy to private ownership.
- Moreover, new investment has been flowing into East Germany, and there are reports that new plants operating in the eastern part of Germany are as profitable as those in the West.
III. The Models and Methods of Simulating the Impacts of Unification
- In this section the authors summarize the models used in the early studies of German unification and give an overview of the approach and results of each of the original studies.
- The last few months of 1989 saw large population flows from the East, and substantial migration continued early in 1990.
- It is likely that a severe slowdown would result in East Germany (still not explicitly part of the model) and that this would lead to pressure on the Bundesbank to ease policy.
- In MX3, the monetary authorities are assumed to move short-term interest rates in response to deviations of a target variable from its targeted level.
- Investment increases due to the higher marginal product of capital in East Germany.
IV. Results from the Models and Key Issues Raised in the Early Studies
- In section III the authors outlined three studies, focusing on the characteristics of the models, the approach to modeling unification, and the issues that were addressed.
- In this section the authors present some key results from each model and draw out some overall lessons from the studies and their implications for model development and policy formulation.
- Table 5 contains standardized results for MULTIMOD, Table 6 contains standardized results for MSG2, and Table 7 contains standardized results for MX3.
- The scenario ordering is based on the original studies and is not necessarily the same across models.
- In the standard trade equations used by most models, exports depend on foreign income and imports depend on domestic income.
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"Coherence scanning interferometry: ..." refers methods in this paper
...The theory that underpins this work is based on a linear theory of 3D imaging that was first published in the context of optical holography by Wolf [12], and Dandliker and Weiss [13]....
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707 citations
491 citations
"Coherence scanning interferometry: ..." refers background in this paper
...CSI typically utilizes broadband, incandescent, or LED sources and Mirau interference objectives to record the interference between the light scattered by the object and that reflected from a reference surface as the objective is scanned though focus [4]....
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Frequently Asked Questions (12)
Q2. What is the reflection coefficient for a perfect conductor?
More generally, the reflection coefficient depends on polarization but the sum of reflection coefficients for orthogonal polarization states is approximately constant for angles of incidence that are less than 45 deg.
Q3. What is the way to explain the scattering process?
For the case of strong surface scattering from the interface between two homogenous media however, providing multiple scattering is negligible, the process can also be considered linear.
Q4. What is the simplest way to explain the scattering of a point source?
It is noted that the scattered field is in general a nonlinear function of the object function ΔB r0 ; however, the process is linearized by assuming that the term Es r0 ; in the integrand is negligible.
Q5. What is the definition of the foil model?
When the surface of a homogenous object is measured, it can be replaced by an infinitely thin foil-like membrane, which has been called the “foil model” of the surface.
Q6. What is the spectral density of the source?
if the spectral density of the source as a function of wavenumber is S k0 , then integrating over all illumination wave vectors, kr, within the numerical aperture and all wavenumbers, k0 that are defined by the function ~GNA −kr; k0 , the output of the CSI can be written~OF k ~ΔF k ~HF k ; (31)where ~H k is the TF and is given by~HF k jkj2 2k · zZZ ~GNA kr; k0 ~GNA k− kr; k0 d3krS k0 dk0.
Q7. What is the reflection coefficient for a dielectric?
For a dielectric, the field at the lower boundary and its gradient may depart markedly from those given in Eqs. (11) and (12) due to propagation through the object.
Q8. What is the effect of the surface scattering approach?
As pointed out by Sheppard in the context of confocal microscopy [24,25], an apparent consequence of the surface scattering approach is that the effective TF (and PSF) of the measuring instrument is modified.
Q9. What is the Kirchhoff approximation for the surface?
In this case the Kirchhoff or physical optics approximation is assumed, which implies that the surface is slowly varying (such that the local radius of curvature is larger than the wavelength).
Q10. What is the significance of a spherical artifact?
More importantly, however, an interferogram 1559-128X/13/163662-09$15.00/0 © 2013 Optical Society of America3662 APPLIED OPTICS / Vol. 52, No. 16 / 1 June 2013of a spherical artifact provides the information necessary to define the resolution of the instrument and, in some cases, compensate for errors introduced by lens aberrations [9].
Q11. What is the definition of the surface scattering approach?
The equations rest on the1 June 2013 / Vol. 52, No. 16 / APPLIED OPTICS 3663assumption of weak scattering, or in other words, that the incident field is weakly perturbed by the object.
Q12. What is the way to deduce the scattering characteristics of a 3D object?
As has been shown elsewhere [17,18], these characteristics can be deduced for a range of far-field measurement instruments, including CSI, if the scattered field is a linear function of the object function, but in general, this is only true if some approximations are made.