text:
Emigration Act, 1983
The Emigration Act, 1982 is an Act passed by the Government of India to regulate emigration of people from India, with the stated goal of reducing fraud or exploitation of Indian workers recruited to work overseas. The Act imposed a requirement of obtaining emigration clearance (also called POE clearance) from the office of Protector of Emigrants (POE), Ministry of Overseas Indian Affairs for people emigrating from India for work. As of 2017, this requirement applies only for people going to one of 18 listed countries.[1][2][3][4]
2 Provisions
2.1 Creation of the office of Protector of Emigrants (Chapter II)
2.2 Registration of recruiting agents (Chapter III)
2.3 Permits for recruitment by employers (Chapter IV)
2.4 Emigration clearance (Chapter V)
2.5 Other provisions
Indians emigrated, both temporarily and permanently, to a number of countries, including the United States, United Kingdom, Germany, Canada, Australia, and the economies of south-east Asia. The bulk of emigration from the 1970s onward was to the Arab states of the Persian Gulf.[3] Recruiting agents played a role in connecting workers to foreign jobs and charged the workers or the employers some share of the revenue. The Emigration Act, 1983 was passed to address concerns related to defrauding and exploitation of workers by the recruiting agents and other problems they might face upon going abroad.[3]
Provisions[edit]
Creation of the office of Protector of Emigrants (Chapter II)[edit]
Chapter II, Section 3 of the Act provided that the Central Government may appoint a Protector General of Emigrants and as many Protectors of Emigrants (POE) as it sees fit, as well as their respective areas of operation. Later Sections of Chapter II defined the duties of Protectors of Emigrants in more detail, provided for emigration check-points, and provided for other emigration officers.[2][3]:7
Registration of recruiting agents (Chapter III)[edit]
The Act made the Protector General of Emigrants and other Protectors of Emigrants the authorities who could register recruiting agents. A person could operate as a recruiting agent for emigrants only if registered. The Act also provided details on the application, terms and conditions, renewal, and cancellation of registration.[2][3]:7
Permits for recruitment by employers (Chapter IV)[edit]
All employers were required to recruit either through a recruiting agent with a valid registration, or obtain a permit for recruitment. The procedure for obtaining, validity period, and cancellation of permits was detailed in the law.[2]
Emigration clearance (Chapter V)[edit]
Any citizen of India seeking to emigrate was required to have emigration clearance from the Protectorate of Emigrants (POE). The application process for emigration clearance, and potential grounds for rejection, were detailed.[2]
As of 2017, passport holders could either have ECR status (emigration check required) in which case they need to obtain emigration clearance, or have ECNR status (emigration check not required) in which case they do not need to obtain emigration clearance.[3] The ECR/ECNR distinction does not appear to have been stated in the original language of the Emigration Act, 1983, which seems to suggest that anybody emigrating for work is required to obtain emigration clearance.[2] The requirements for getting to ECNR status have been progressively relaxed over time, starting from being restricted to people such as graduates and income tax payers and now applying to a much wider set of people including those who have completed matriculation (class 10 of school).[5][6]
Other provisions[edit]
Chapter VI described the appeals process
Chapter VII provided details on offences and penalties
Chapter VIII covered miscellaneous items
^ "ECNR/ECR". Bureau of Immigration, Ministry of Home Affairs, Government of India. Retrieved December 10, 2017.
^ a b c d e f "The Emigration Act, 1983 Alongwith The Emigration Rules, 1983, As Amended by Emigration (Amendment) Rules, 2004 vide GSR 143(E), dt. 26-2-2004, w.e.f. 15-3-2004" (PDF). Retrieved December 10, 2017.
^ a b c d e f "Emigration and You" (PDF). Government of India. Retrieved December 10, 2017.
^ "The Emigration Act, 1983" (PDF). Government of India. Retrieved December 10, 2017.
^ "What does ECR and ECNR mean on an Indian passport?". Quora. Retrieved December 10, 2017.
^ Ravikaran, G. (November 29, 2006). "ECNR stamp not required for class 10 graduates". The Hindu. Retrieved December 10, 2017.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Emigration_Act,_1983&oldid=874331223"
1983 in India
This page was last edited on 18 December 2018, at 16:00 (UTC).


Robert Baker MRICS FAAV has been promoted to be joint front line auctioneer selling stirks at Sedgemoor Auction Centre – one of the country's largest livestock markets.
Auctioneers Greenslade Taylor Hunt run the market and have also promoted Robert to Associate within the firm.
Robert works out of Greenslade Taylor Hunt's Burnham-on-Sea office and can be contacted on 01278 765588.


We've all been there – you're sitting at our desk and realize that you've run into an IT issue that's preventing you from being able to proceed with our day. Whether it's being unable to print an important report for a meeting, or being unable to log in to your computer, there's a bevy of issues that can arise.
Fortunately, many of the issues that will stop you in your tracks are relatively easy to solve. While some issues do necessitate the creation of a help desk ticket, there are others that we frequently experience that actually have pretty quick fixes. So quick, in fact, that you can try them out for yourself and skip the ticket all together.
Without further ado, here are some of the most common questions that run across our help desk board, and their easy solutions.
We probably see some variation of this problem no less than 10 times per week. Seriously. However, just because we're constantly getting tickets for printer issues doesn't mean they're complicated – here are some of the easiest things to check and try before putting in a ticket.
Still no luck? Then it's time to open a ticket.
When we get tickets from users unable to log into their computers, the urgency (and panic) is quite high – in today's digital age, our entire workflow comes to an abrupt halt when we're unable to log into our PCs.
Please Note: Read this section thoroughly before entering your passwords. Too many failed attempts can lock you out and necessitate a ticket when all you needed initially was to click off your caps lock. So give this a read, check your settings and features, and then proceed with entering your password.
First, check to see if your caps lock is on. Passwords are case-sensitive, so correcting this tiny error will save you from frustration. Similarly, make sure your number lock ("num lock") is on if your password contains numbers and you're using the 10-digit keypad.
If your caps lock situation is squared away, stop for a tick and make sure you're using the correct password. Did your system ask you to change your password yesterday and you've forgotten about it already?
Next up – reboot. Honestly, anytime your computer starts acting wonky, you should reboot. It's going to be one of the first things any IT professional asks you, so if you do it without being asked you'll be ahead of the game! Also, it's possible that a patch or update went through since you last logged on that requires a reboot and is holding up your system.
Does your keyboard have batteries? Is it connected properly? You may notice that not only are you unable to login, but you're unable to even begin typing your password. If you have a Bluetooth connected keyboard then check to make sure your batteries aren't dead. If you've got a keyboard that connects via USB drive, make sure the plug is secure – once you've fixed your connectivity issues you should be able to type away.
Of course, if none of these seem to be the issue then give us a call and we'll see what we can do to get everything sorted out and get you on your way. If your screen displayed any error messages while trying to log in, take note of those as your Engineer will probably ask you about them.
Many of the "Internet Issues" tickets that we get tend to involve users connecting to Wi-Fi either in the office or while working remotely.
First thing's first – if you're having Wi-Fi connectivity issues, reboot your computer. If that doesn't do the trick, then – if possible – reboot the Wi-Fi. If neither of those options work, then a help desk ticket is in order.
Please note that you should only reboot the network hardware if you are authorized to do so (ie: you're in your own home or your internal IT department is on-board with it).
As you can see there are generally a few things you can do prior to submitting a ticket that may remedy the issue and have you happily on your way to productivity. If you've taken a look at our recommendations and they don't seem to be working, or don't apply to your particular situation, then give us a call and we'll start a help desk ticket.


text:
Q: Dynamic Match Variable Mongodb I want to be able to pass a dynamic BSON variable to match for mongodb.
Here is what I have tried:
var query = "\"info.name\": \"ABC\"";

and
var query = {
    info: {
        name: "ABC"
    }
}

Neither of these work when passing variable 'query' to match (like below):
$match: {
   query
}

but explicitly passing like below does work:
$match: {
   "info.name": "ABC"
}

A: It works when you pass a query object that is like;
var query = {
    "info.name": "ABC"
}

and passed into the aggregation pipe like so;
{ $match: query }

You can see its details on MongoDB Node.js Driver Tutorials

You cannot use a JSON object to query nested fields, like;
var query = {
    info: {
        name: "ABC"
    }
}

check here
unless info contains only name field, then it can be used in such a manner. But again you have to pass with { $match: query }, like here

A: Here is what went wrong
var query = "\"info.name\": \"ABC\"";
{ $match: ""info.name": "ABC"" } // This is single string

Here in this query, we get single string that's why not result filter
But when you are using explicitly passing like this "info.name": "ABC" it work
For data
{
  _id: ObjectId(XXXXXXXXXX),
  info: { name: "ABC" }
}

You can use this aggregate query
// Create object and use this into [$match][1] stage
   const data = { "info.name": "ABC" };
// Use this object in match stag
         .aggregate([{ $match: data}])

if you have array of object then you need to use $elemMatch
For data
 {
     _id: ObjectId(XXXXXXXXXX)
     info: [{ name: "ABC" }, { name: "DEF" } ]
}
// use elemMatch if array of object
     .aggregate([{ $match:  { info: { $elemMatch:{ name:  "ABC" }}}}])

A: As MongoDB documentation says:

To specify a query condition on fields in an embedded/nested document, use dot notation.

The actual problem is that you have your object property name as a variable in your JS code. Please, check how to add a property to a JavaScript object using a variable as the name.
Here is how you can do it:
var propertyName = "info.name"
var query = {}
query[propertyName] = "ABC"
...

redpajama_set_name: RedPajamaStackExchange


Finally a picture of the Coal Aruba Hot Class Tank we heard about in product alerts last week. I love it and will be getting it but I also wish lulu had made a solid Aruba version. I really like how the lower bodice of this tank, made of Sheer Luon Jersey, softens the colors so they look heathered. Aruba would have been so pretty in the sheer luon. I also think having it in a solid color makes it more casual wear and not so athletic. No bother, I know this will be my Aruba item and I do like the combination of Aruba with Black/Coal.
and Coal Strata Wunder Unders.
"Spotted! Sandra Bullock in Head To Toe Lululemon"


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text:
July 21, 2022 ResearchSteve Panton
Summary: based on a comparison with eight similar metropolitan art institutes across the United States, the DIA produces one-third as many exhibitions as would be expected from an institution with its financial and physical resources.
Background: A visitor to the Detroit Institute of Arts in mid-July 2022 would have seen a total of two exhibitions. The first was an annual show of work by Detroit-area School students. The second was a small installation of paintings and works on paper created by contemporaries of Van Gogh.
Given the resources available to the DIA, including the ~$30M/year funding provided by the public through the tri-county millage, a total of just two relatively minor exhibitions seems a bafflingly low level of programming activity.
This study examines whether the situation described above is typical of what visitors to an art institute in a major city might expect to encounter. It looks at the DIA's long-term cultural productivity by aggregating the total number of exhibitions launched by the DIA from January 2013 to December 2021 in comparison to similar institutions in eight like-sized American metropolitan areas.
The starting point of January 2013 was chosen since it marks the beginning of the millage funding period, and hence the study is examining the amount of exhibition programming that the residents of Macomb, Oakland, and Wayne Counties have received in return for their property taxes.
The benchmark also summarizes the resources available to each institution in terms of gallery space and total salaries (normalized to the Detroit cost of living.)
The results show that the DIA is:
=> Fifth highest in available gallery space,
=> Second highest in salary costs (normalized to Detroit cost of living)
=> Lowest in terms of the number of exhibitions produced.
A striking comparison point is the Minneapolis Institute of Art, which has approximately the same gallery space and total salary bills but which produced three times as many exhibitions over the study period.
Indeed, if the visitor described in the first paragraph had been at the Minneapolis Institute of Art, rather than the DIA, they would have seen a total of sixteen exhibitions rather than two, a quite staggering disparity.
Another way of examining the data is to show the DIA in comparison to the average of the eight other institutions. When you look this way, the data shows that in comparison to the average of the other eight institutions, the DIA has
==> 22% more gallery space,
==> 46% higher salaries (normalized to Detroit cost of living)
==> 49% fewer exhibitions.
In simple terms, DIA is producing approximately one-third as many exhibitions as might be expected from an institution with its financial and physical resources.
Certainly, not all exhibitions are of equal stature, and exhibitions are not the only value the DIA provides beyond exhibiting its core collection, but even with these qualifications, this is a staggering statistic that warrants explanation.
Metropolitan areas with comparable population sizes were taken from here.
The closest equivalent institution to the DIA was identified in each city
The gallery square footage for each institution was taken from here or from the institution's own website. The gallery square footage for the Pheonix Art Museum was not found but estimated at 1/3 of the total square footage of the building.
Total salaries for each institution were taken from the I990 for the last full financial year before the pandemic. Note that the High Museum figure was taken directly from the Woodruff Art Center's annual report.
Salaries were normalized to the Detroit cost of living using a standard cost of living calculator.
The number of exhibitions that had a start date from 1/1/13 – 12/31/21 was counted directly from each institution's website. Note that PAM exhibitions for 2013/4/5 were unavailable and were pro-rated from subsequent years. The DIA exhibitions for 2013/4/5 were counted from archived copies of the DIA's website.
← 160 Ijania Cortez Research – Public and Philanthropic funding for Arts and Culture in Metro Detroit / Part 1 : Overview →

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}
Multiphase flow is a typical flow, and bubble characteristic measurement is of great importance to discover the flow mechanism and guide the practical fluid mechanical engineering \cite{ZHENG20105264}. With the development of computer and optoelectronic techniques, visual inspection \cite{HONKANEN201025, WU20132928} based on photography has been widely used in multiphase flow measurement. However, the overlapping or opaque objects, which would decrease the reconstruction accuracy of modality and motion feature parameters of bubbles in gas-liquid two-phase, exist widely and cannot be recognized effectively. From the past studies, virtual binocular stereo vision has been applied by Xue et al. \cite{Xueting, Xueting2}, who did an experiment by using one camera and 4 mirrors to match and reconstruct bubble trajectory motion in a glass-made water tank from two direction. The mirror-based approach was applied in numerous single-camera stereovision techniques in various fields \cite{YU2016120, PAN201625, YU201717}. And Pan et al. optimized the parameters of the proposed 3D-DIC system, including the 3D position and orientation of the camera, effective focal length, principle point coordinates, and lens distortion coefficients \cite{Pan44412}. Inspired the emerging studies of the single-camera mirror-based stereo image correlation technique \cite{Pan2018}, a 3D imaging device combining single camera and multi-mirror was presented for capturing the comprehensive multiphase flow images information with an opaque object in the center of the observation area. And its design arrangement is a multi-objective problem (MOP), which is necessary to be optimized.

For solving the multi-objective problem, there are a variety of available algorithms \cite{app8071144, app8020175}, including genetic algorithm (GA), particle swarm optimization algorithm, artificial fish swarm  algorithm, and harmony search algorithm. HS algorithm was proposed and established first in 2001 by Geem et al. \cite{Zong600201}, which simulated the process of improvisation music, that is, the music player adjusts the performance to a wonderful harmony state through impromptu music adjustment. Harmony algorithm in the application of MOP, the search for the optimal solution is rather similar to the production of offspring in GA with mutation and crossover operations. The decision variables in the target problem are similar to the pitch of each instrument. The HS algorithm is a heuristic global search algorithm which also has the advantages of less parameters and high efficient calculation \cite{WANG20102826}.

As for the application of harmony algorithms in the MOP problems, many researchers have applied it in various areas, such as the location, size and power factor of Distributed Generation \cite{RN1552}, the multi-objective flexible job shop scheduling problem \cite{RN1542}, the scheduling problem of hydraulic systems pump \cite{RN1539, RN1550}, the urban traffic light scheduling problem \cite{RN1541} and so on.
However, empirical studies have shown that the original harmony search algorithm in dealing with multi-objective constrained optimization problems is being subject to certain restrictions \cite{PAN2010830, RN1538}. To overcome these shortcomings, utilization of a modified harmony search algorithm for multi-objective optimization to optimize the shielding effectiveness of wheel for secondary development is necessary.

Dai et al. \cite{RN1538} improved HS to solve the trouble for novice users about the parameters which need to be set by users according to experience and problem characteristics. Amaya et al. \cite{RN1536} presented a novel modification of the Harmony Search (HS) algorithm which is able to self-tune as the search progress. Yuan et al. \cite{RN1557} integrated HS in the research of the weakness about parallel chaos optimization algorithm, which aims to obtain optimum solution accurately. Meysam Gheisarnejad \cite{RN1544} developed cuckoo optimization algorithm into HS algorithm to design a secondary controller for two practical models of load frequency control problem. Gao et al. \cite{gao2009uni} propose two modified HS methods to deal with the uni-modal and multi-modal optimization problems. The first employed a novel HS memory management approach to handle the multi-modal problems and the second utilized the Pareto-dominance technique, which targets at the constrained problems. The MOP of the single-camera-multi-mirror device concerns multiple constraint conditions. In this paper, the two modified HS methods were applied and integrated into one improved HS algorithm, which absorbs the advantages in both two HS methods.

\section{Optimization Algorithm}
It is known that when experienced musicians compose a harmony, it is usually by trying various possible combinations of the music pitches stored in memory. This kind of effective search for a perfect harmony is analogous to the procedure of finding an optimal solution in engineering problems. The HS method is inspired by the working principles of the harmony improvisation \cite{Zong600201}. And as shown in Figure \ref{fig09} the flowchart of the basic HS method was presented.
\begin{figure}[htbp]
  \centering

  \includegraphics[width=10cm]{09.jpg}\\
  \caption{Flowchart of the basic HS method}\label{fig09}
\end{figure}

The initial HS Memory (HM) consists of a given number of randomly generated solutions to the optimization problems under consideration. For a n-dimension problem, a HM with the size of HMS can be represented as follows:

\begin{equation}\label{eqHM}
  {\rm{HM = }}\left[ {\begin{array}{*{20}{l}}
{x_1^1,x_2^1, \cdots ,x_N^1}\\
{x_1^2,x_2^2, \cdots ,x_N^2}\\
 \vdots \\
{x_1^{HMS},x_2^{HMS}, \cdots ,x_N^{HMS}}
\end{array}} \right]
\end{equation}
where,$\left[ {x_1^i,x_2^i, \cdots ,x_n^i} \right]$$(i = 1,2, \cdots ,HMS)$is a candidate solution.

The basic harmony search method is difficult to find optimum result of multi-objective problem because in the iterative process, the harmony memory members easily stop in local optimal solution. Therefore, it is important to maintain the diversity of HM.

Assuming the current HM fitness value is expressed as ${f_i}(i = 1,2, \cdots ,HMS)$ and after a new candidate solution $\left( {{{x'}_1},{{x'}_2}, \cdots ,{{x'}_n}} \right)$ as fitness, then the distance ${d_i}\left( {i = 1,2, \cdots ,HMS} \right)$ between it and all other HMs is expressed as following equation:
\begin{equation}\label{eqdi}
    {d_i} = \left\| {\left[ {{{x'}_1},{{x'}_2}, \cdots ,{{x'}_n}} \right] - \left[ {x_1^i,x_2^i, \cdots ,x_n^i} \right]} \right\|
\end{equation}

Besides, the average fitness value of HM is expressed as follow:
\begin{equation}\label{eqF}
   \overline F  = \frac{{\sum\limits_{i = 1}^M {{f_i}} }}{M}
\end{equation}
where, $M$ is the number of the HM members.

Though for the concept of ${d_i}\left( {i = 1,2, \cdots ,HMS} \right)$  must prevent the excessive similarity between the members from HM. In other word, modified HS would be suitable for handling multi-objective problem by maintaining the diversity of HM. Most of the practical optimization problems are in fact constrained optimization problems, whose goal is to find the optimal solution that satisfies a set of given constraints \cite{Miettinen2008, CHEN20113336}. In general, a constrained optimization problem is described as follows:

Find $ \mathbf{x} = \left( {{{x'}_1},{{x'}_2}, \cdots ,{{x'}_n}} \right)$ to satisfy:
\begin{equation}\label{eqminf}
  \begin{array}{l}
minf(\mathbf{x})\\
{\rm{s}}{\rm{.t}}{\rm{.}}\left\{ \begin{array}{l}
{g_i}(\mathbf{x}) \le 0,i = 1,2,3 \cdots I\\
{h_j}(\mathbf{x}) = 0,j = 1,2,3 \cdots J
\end{array} \right.
\end{array}
\end{equation}
where, $f(\mathbf{x})$ is the objective function, $g_i(\mathbf{x})\leq0$ and $h_j(\mathbf{x})=0$ are the inequality and equality constraint functions respectively. As a matter of fact that the equality constraint functions can be easily transformed into the inequality constraint functions:
$$|h_j(\mathbf{x})|\leq\varepsilon$$
where, $\varepsilon$ is a small enough tolerance parameter. Therefore, we only consider the inequality constraint functions $g_i(\mathbf{x})\leq0$, $i = 1,2,3 \cdots,I$. Since the constraint functions could divide the whole search space into some disjoint islands such problems are generally difficult to deal. Numerous constraint-handling techniques have been investigated during the past decades. One popular solution is to define a new fitness function $F(\mathbf{x}))$ to be optimized. For example, $F(\mathbf{x}))$ is the combination of the objective function $f(\mathbf{x}))$ and weighted penalty terms $P(\mathbf{x}))$, $i = 1,2,3 \cdots I$, which reflect the violation of the constraint functions:
\begin{equation}\label{eqFx}
  F({\rm{x}}) = f(x) + \sum\limits_{i = 1}^I {{w_i}} {P_i}(x)
\end{equation}
where $w_i$, $i = 1,2,3 \cdots I$, are the preset weights. The overall optimization performance depends on the penalty terms and their weights, and may significantly deteriorate with inappropriately chosen ones.

Besides, the HM only stores the feasible solution candidates. The new HM members are generated either from the existing HM members or in a random way. Nevertheless, those are not guaranteed to always meet all the constraints. In the original HS method, the new HM members satisfying the constraints can be obtained based on only trial and error method which may lead to a time consuming procedure particularly in the case of multiple and complex constraint functions.

In this improved HS algorithm, the advantage of those HM members that do not even meet the constraints is taken. The key issue is how to rank the HM members according to their objectives as well as constraint functions values. The HM members are divided into two different parts: feasible members and infeasible members. The former satisfy all the constraint functions while the latter do not. The ranking of the feasible HM members is straightforward that means they can be sorted using their objective functions values. However, for the infeasible ones, the ranking is based on the Pareto dominance of these HM members \cite{COELLOCOELLO2002193, Mateo2012}. An infeasible HM member dominates another, if none of its constraint functions values are larger and at least one is smaller. Formally, the Pareto dominance is defined as follows.

Suppose there are two infeasible HM members $\mathbf{x}^a$ and $\mathbf{x}^b$. If
$\forall i \in \{1,2,\cdots, I\}$, $g_i(\mathbf{x}^a)\leq g_i(\mathbf{x}^{b})\bigcap \exists i \in \{1,2,\cdots, I\}$, $g_i(\mathbf{x}^a)< g_i(\mathbf{x}^{b})$, it can be concluded that $\mathbf{x}^a$ dominates $\mathbf{x}^b$. For each infeasible HM member, we can calculate the number of the others that dominate it. That implies its relative degree of violation of the constraint functions. It is the ranking of an infeasible HM member and is determined by the number of other infeasible HM members by which it is dominated.

Once after the whole HM has been ranked, the worst HM member $\mathbf{x}^\#$ can be selected and compared with the new solution candidate $\mathbf{x}^*$. Note, $\mathbf{x}^*$ does not need to be feasible. When $\mathbf{x}^\#$ is compared with $\mathbf{x}^*$, $\mathbf{x}^*$ will replace $\mathbf{x}^\#$ only in one of the following three cases:

\textbf{Case 1}: $\mathbf{x}^*$ is feasible, and $\mathbf{x}^\#$ is infeasible.

\textbf{Case 2}: Both $\mathbf{x}^*$ and $\mathbf{x}^\#$ are feasible and $f(\mathbf{x}^*)<f(\mathbf{x}^\#)$.

\textbf{Case 3}: Both $\mathbf{x}^*$ and $\mathbf{x}^\#$ are infeasible and $\mathbf{x}^*$ dominates $\mathbf{x}^\#$.

The process is shown in Figure \ref{fig03}.
\begin{figure}[htbp]
  \centering

  \includegraphics[width=12cm]{03.jpg}\\
  \caption{ Multi-objective optimization flowchart based on a modified HS algorithm}\label{fig03}
\end{figure}
\section{Design Expression of the Single-camera-multi-mirror Device}
\subsection{Measurement Principle of the 3-D Imaging}

\begin{figure}[htbp]
  \centering

  \includegraphics[width=8cm]{02.pdf}\\
  \caption{Schematic diagram of the 3-D imaging principle}\label{fig02}
\end{figure}

Figure \ref{fig02} shows the arrangement of the single-camera-multi-mirror device from the top view. The square the outer contour of the object being observed. The blue circle is the area that needs to be photographed. And the red circle is the area that was opaque. Using a single camera from one direction cannot capture the comprehensive image information of the blue area, because of the opaque object. To solve this problem, a novel single-camera-multi-mirror device was designed to enable one camera to capture the images from four vertical faces of a cuboid. The images of the 4 faces were reflected by the plane mirrors and focused on the camera lens.

To eliminate the image refringence caused by the oblique angle between the observed face and the virtual camera, the light center axes of the three virtual cameras were all defined to be perpendicular to the observed faces. Besides, the distance of the optical path of the four virtual cameras were set to be equal to ensure the consistent image resolution from the four sides and enable the lens to focus to the four observing areas.

\subsection{Mathematical Model of the Single-camera-multi-mirror Design}
\begin{figure}[htbp]
  \centering

  \includegraphics[width=12cm]{01.pdf}\\
  \caption{Establishment and parameter setting of the mathematical model}\label{fig01}
\end{figure}

To optimize the arrangement of the high-speed camera and six plane mirrors to build the mathematical model for optimization, the design diagram was drawn, as shown in Figure \ref{fig01}. The point $P$ and $Q$ are the position of the virtual camera 3 and 2  in Figure \ref{fig02}.
Due to the symmetrical relationship of the virtual camera 1  and 2, the optimal design of the two mirrors of virtual camera 1 and 4 was omitted. So the optimization design variables in practice were the position parameters of the camera (point $H$) and the three mirrors (marked as A, B and C). The radius of the observing area is defined as $r$. The length of the outline of the observed cuboid is defined as $l_V$. So, the coordinate of the point $V_0$ is $(\frac{l_V}{\sqrt{2}},0)$. The default unit in this paper is mm.

The coordinates of the virtual camera 2 and 3 are expressed as follows:
$ Q(\frac{b+c+d}{\sqrt{2}},-\frac{b+c+d}{\sqrt{2}}) $,
$ P(\frac{b+c+d}{\sqrt{2}},\frac{b+c+d}{\sqrt{2}}) $.
Besides, the coordinates of the plane mirrors A and B can be expressed as
$ A(\frac{b}{\sqrt{2}},\frac{b}{\sqrt{2}}) $, $ B(\frac{b}{\sqrt{2}},-\frac{b}{\sqrt{2}}) $.

The three angle optimization variables are defined as follows $\theta_1$ (mirror A), $\theta_2$ (mirror B) and $\theta_3$ (mirror C). The equations for the lines crossing the A and B mirrors are respectively dissected as follows:
$$ L_A: y=x\tan\theta_1+\frac{a}{\sqrt{2}}(1-\tan\theta_1) $$
$$ L_B: y=x\tan\theta_2-\frac{b}{\sqrt{2}}(1+\tan\theta_1) $$

As point $P$ and point $H$ are symmetrical about line $L_A$, the coordinates of $H$ are obtained as follows:
\begin{align*}
x_H&=x_P+y_P\tan\theta_1-y_H\tan\theta_1\\
y_H&=\frac{ 2x_P\tan\theta_1+y_P(\tan^2\theta_1-1)+\sqrt{2}a(1-\tan\theta_1)  }
    {1+\tan^2\theta_1}
\end{align*}

Due to $x_P=y_P$ and $x_H=0$, the following equation is obtained:
$$ d=-b-c+a\frac{ 2(\tan\theta_1-\tan^2\theta_1)}
    {1+2\tan\theta_1 -\tan^2\theta_1} $$

Similarly, because point $Q$ and point $R$ are symmetrical about line $L_B$, the coordinates of $R$ are obtained as follows:
\begin{align*}
x_R&=x_Q+y_Q\tan\theta_2-y_R\tan\theta_2 \\
y_R&=\frac{2x_Q\tan\theta_2+y_Q(\tan^2\theta_2-1)-\sqrt{2}b(1+\tan\theta_2)}
    {1+\tan^2\theta_2}
\end{align*}

The equation of line $L_{BR}$ can be obtained from two points $B$ and $R$.
$$ L_{BR}: y=\frac{y_B-y_R}{x_B-x_R}(x-x_R)+y_R $$

As point $C_P$ is the midpoint of the line segment $RH$, the coordinates of the point $C$ are $(\frac{x_R+x_H}{2},\frac{y_R+y_H}{2})$ and the equation of line $L_C$ can be expressed as:
$$ L_C: y=\tan\theta_3(x-\frac{x_R+x_H}{2})+\frac{y_R+y_H}{2} $$

As the point $C$ is the intersection of Line $L_C$ and Line $L_{BR}$, the coordinates of the point $C$ are obtained as follows:
\begin{align*}
x_C&=\frac{ \frac{y_B-y_R}{x_B-x_R}x_R-y_R-\frac{x_R+x_H}{2}\tan\theta_3+\frac{y_R+y_H}{2} }
    { \frac{y_B-y_R}{x_B-x_R}-\tan\theta_3 }\\
y_C&=\frac{y_B-y_R}{x_B-x_R}(x_C-x_R)+y_R
\end{align*}

In addition, as the line $L_C$ is perpendicular to $L_{BR}$, the following equation can be obtained:

\begin{equation}\label{eq154}
  \tan\theta_3\cdot\frac{y_R-y_H}{x_R-x_H}=-1
\end{equation}

Based on the coordinates of the point $B$ and $C$, the geometrical relationship must be met:

\begin{equation}\label{eq159}
  c=|BC|=\sqrt{(x_B-x_C)^2+(y_B-y_C)^2}
\end{equation}

The relative coordinate values of the points of $B$, $C$, $R$ and $H$ can be all derived, when the design parameters $a$, $b$, $c$, $\theta_1$, $\theta_2$ and $\theta_3$ are given. So, the $\theta_2$ and $\theta_3$ can be obtained by solving the function set of Equation \ref{eq154} and \ref{eq159}.
\begin{equation}
\left\{
\begin{split}
&x_H-x_R+\tan\theta_3(y_R-y_H)=0\\
&x_C(x_C-2x_B)+y_C(y_C-2y_B)+b^2-c^2=0
\end{split}
\right.
\end{equation}

In above, the optimization variables are $a$, $b$, $c$ and $\theta_1$. All the position and angles can be derived by giving a set of values of these 4 variables.

\subsection{Optimization Model}
The optimal arrangement of the 3D imaging device in this paper is a multi-objective constraint optimization problem. The resolution of the experiment videos was limited by the capability of the high-speed camera and the distance from the observed field to the camera lens. The resolution capability of the camera and the lens used in the experiment are fixed. The cavitation bubbles in the valve were quite small. In order to ensure the resolution of the bubble images, the distance of the optical path were optimized as short as possible. Then, the first optimization objective can be expressed as follows:
\begin{equation}\label{eqf1}
  f_1(\mathbf{x})=b+c+d
\end{equation}

Besides, the overall size of the 3D imaging device should be as compact as possible. The vertical length is defined as the second optimization objective:
\begin{equation}\label{eqf2}
  f_2(\mathbf{x})=x_B
\end{equation}
And the lateral length is defined as the third optimization objective:
\begin{equation}\label{eqf2}
  f_3(\mathbf{x})=y_A-y_H
\end{equation}

The objective function is mathematically defined by:
\begin{equation}
\min J(\textbf{x})=\min(f_1(\mathbf{x}),f_2(\mathbf{x}),f_3(\mathbf{x}))
\end{equation}
Subject to:
$$G(\mathbf{x})\leq0 $$
where $\textbf{x}=[a,b,c,\theta_1]^T$.

\subsection{Model Constraint}
The calculation of the following parameters was to define the constraint conditions to meet the geometrical requirements of the single-camera-multi-mirror design and ensure no interference between the optical paths.

To prevent the optical image reflected by the mirror A from being interrupted by the valve, there should be a certain interval between $A_0$ and $V_0$, as expressed in Equation \ref{eqxA0}:
\begin{equation}\label{eqxA0}
  x_{A_0}-x_{V_0}>3
\end{equation}

The left boundary of the optical path reflected by the mirror C is on the positive side of the $y$ axis, in case of influencing the mirror belonging to the virtual camera 1, which is symmetrical with the mirror C. So, the $x$ coordinate of the point $C_1$ should meet the following constraint:
\begin{equation}
  x_{C_1}>2
\end{equation}

The slope of the line $HC_2$ and $HV_0$ can be expressed as:
$$ k_{HC_2}=\frac{y_H-y_{C_2}}{x_H-x_{C_2}},\ k_{HV_0}=\frac{y_H-y_{V_0}}{x_H-x_{V_0}} $$
To prevent the optical path from the mirror A and C from interfering with each other, the slopes angle of the line $HC_2$ and $HA_1$ should meet:
\begin{equation}
\arctan k_{HC_2}-\arctan k_{HV_0}>1^\circ
\end{equation}

To prevent interference between the placement of the mirror C and the valve body, the position of the points $C_1$ and $C_2$ should meet:
\begin{equation}
    y_{C_1}-y_{K_1}<-30
\end{equation}
\begin{equation}
    y_{C_2}-y_{K_2}<-10
\end{equation}

The visual scope is limited by the viewing angle of the camera lens. So,
\begin{equation}
   \beta<17.5^\circ
\end{equation}
Above all, the constraint can be defined as:
$$G(\mathbf{x})=\{g_1(\mathbf{x}),g_2(\mathbf{x}),g_3(\mathbf{x}),g_4(\mathbf{x}),g_5(\mathbf{x}),g_6(\mathbf{x})\}^T$$
\noindent where,
\begin{equation*}
\left\{
\begin{split}
&g_1(\mathbf{x})=\arctan k_{HV_0}-\arctan k_{HC_2}+1^\circ\\
&g_2(\mathbf{x})=x_{V_0}-x_{A_0}+3\\
&g_3(\mathbf{x})=2-x_{C_1}\\
&g_4(\mathbf{x})=y_{C_1}-y_{K_1}+30\\
&g_5(\mathbf{x})=y_{C_2}-y_{K_2}+10\\
&g_6(\mathbf{x})=\beta-17.5^\circ\\
\end{split}
\right.
\end{equation*}
\section{Case Study}
\subsection{3D multiphase flow imaging of a water hydraulic valve}
In this section, the optimization arrangement of the 3D imaging device was applied in the multiphase flow reconstruction of the 3D cavitation bubble cluster in a water hydraulic valve. The main materials of the valve body is a type of transparent thermoplastic called Polymethylmethacrylate (PMMA, Perspex, acrylic glass). The two basic structural dimensions is given as $r=17$ and $l_V=118$ (unit: mm). Besides, there is the valve core in the center of the observed area, which obscured quite much sight. Because of the inevitable space for connecting the inlet/oulet hydraulic pipes, there is no space for the mirror in practice, and the virtual camera 4 was omitted.

The linear constraints of design parameters are defined according to the design requirements as follows.
\begin{equation}
\left\{
\begin{split}
&150<a<400\\
&150<b<400\\
&150<c<400\\
&145^\circ < \theta_1<180^\circ\\
\end{split}
\right.
\end{equation}

\begin{figure}[htbp]
  \centering

  \includegraphics[width=10cm]{10.pdf}\\
  \caption{Optimization variables versus iterations during the optimization process}\label{fig10}
\end{figure}
\begin{figure}[htbp]
  \centering

  \includegraphics[width=10cm]{11.pdf}\\
  \caption{Objective functions versus iterations during the optimization process}\label{fig11}
\end{figure}

The relevant parameters in the HS algorithm are as follows: HMS=50, HMCR=0.75, PAR=0.4. The number of the Pareto solution is equal to 10. The number of iterations is 100 times, while 20 new sets of the optimization variables' solutions will replace the worse solutions in each iteration.
The changes of the variables and objective functions during the optimization procedure are illustrated in Figures \ref{fig10} and \ref{fig11}. As shown in Figure \ref{fig11}, in the first 20 iterations, the value of $f_1$, $f_2$ and $f_3$ were greatly fluctuate. After that, all the three objective functions steadily decreases and converges. This shows the efficiency of the algorithm in convergence speed. As a result, Table \ref{tab01} gives the Pareto results acquired.

\begin{table}[htbp]
  \small
  \centering
  \caption{Pareto resolutions of optimization}\label{tab01}
    \begin{tabular}{cccccccc}
    \hline
    No. & $a$/mm & $b$/mm  & $c$/mm  & $\theta_1$/rad & $f_1(\mathbf{x})$/mm  & $f_2(\mathbf{x})$/mm  & $f_3(\mathbf{x})$/mm  \\
    \hline
    1     & 187.879  & 255.392  & 181.091  & 2.612  & 680.596  & 180.589  & 474.469  \\
    2     & 188.501  & 254.701  & 179.621  & 2.613  & 684.255  & 180.101  & 477.499  \\
    3     & 189.329  & 257.592  & 184.673  & 2.610  & 678.156  & 182.145  & 470.137  \\
    4     & 189.329  & 255.584  & 177.641  & 2.611  & 679.927  & 180.725  & 471.979  \\
    5     & 189.329  & 257.440  & 183.339  & 2.611  & 679.927  & 182.038  & 471.979  \\
    6     & 189.329  & 257.338  & 183.339  & 2.611  & 679.927  & 181.966  & 471.979  \\
    7     & 189.185  & 260.852  & 181.046  & 2.610  & 677.640  & 184.451  & 469.780  \\
    8     & 189.329  & 257.195  & 178.050  & 2.611  & 679.927  & 181.864  & 471.979  \\
    9     & 189.185  & 260.852  & 181.046  & 2.610  & 677.640  & 184.451  & 469.780  \\
    10    & 189.185  & 260.852  & 181.046  & 2.610  & 677.640  & 184.451  & 469.780  \\
    \hline
    \end{tabular}%
  \label{tab:addlabel}%
\end{table}%

\begin{figure}
  \centering

  \includegraphics[width=12cm]{12.jpg}\\
  \caption{GUI of the optimizations design}\label{fig12}
\end{figure}

In order to facilitate other designers to apply the optimization method presented in this paper, a graphical user interface (GUI) was developed as shown in Figure \ref{fig12}, which integrated the functions of inputting the initial object parameters, running the modified HS algorithm, displaying the optimization results and drawing the optimal arrangement design. As a result, the optimal solution is obtained and selected as follows:
\begin{equation}
\begin{split}
\textbf{x}_{opt}=&[a_{opt},b_{opt},c_{opt},\theta_{1opt}]^T\\
=&[187.879, 255.392, 181.091, 149.679^\circ]^T
\end{split}
\end{equation}

\begin{figure}
  \centering

  \includegraphics[width=12cm]{04.jpg}\\
  \caption{3D imaging experiment of the transparent water hydraulic valve}\label{fig04}
\end{figure}

Figure \ref{fig04} shows the photographs of a 3D imaging experiment. As shown in Figure \ref{fig04}(a), the water hydraulic experimental setup consisted of the water hydraulic platform, industrial personal computer (IPC), and the 3D imaging device. The transparent water hydraulic valve used as the observation object was shown in Figure \ref{fig04}(b). The arrangement design drawing was printed on an A2 sheet of paper. As shown in Figure \ref{fig04}(c). five plane mirror and a high-speed camera were placed based on the printed design paper. From the front view, the images from three sides of the valve was captured.
\subsection{Algorithm Performance}
To testify the good performance on locating most of the local optima in addition to the global optimum, the Pareto data of every iteration was collected. 2000 arrangement solutions of the 3D imaging device were recorded. The position of the mirror C were decided by the coordinate of the point $C$. Point $A$, $B$ and $H$ can only move on a certain line, while point C can move within a certain area.  And both $x_C$ and $y_C$ were decided by the optimal variables $a$, $b$, $c$,$\theta_1$, which can comprehensively reflect the performance. So we select point $C$ to analyze its position distribution and density.

\begin{figure}
  \centering

  \includegraphics[width=8cm]{08.jpg}\\
  \caption{Kernel density of the point $C$}\label{fig08}
\end{figure}
Figure \ref{fig08} shows the density analysis of the point $C$. The 10 Pareto solutions were more concentrated in the pea-shaped area around the optimal solution.

\begin{figure}
  \centering

  \includegraphics[width=12cm]{07.jpg}\\
  \caption{Position distribution of point $C$ and its optimization objectives' value}\label{fig07}
\end{figure}
Figure \ref{fig07} illustrates the contour maps of the optimization objectives' values about point $C$. The red star symbol is marked as the optimal position of the point $C$. The distribution of the point $C$ is quite extensive, which indicates that there were spread selections considered as the optimal solutions.
Compared Figure \ref{fig07}(b) with Figure \ref{fig07}(a) and (C), the area of the relative small value of the $f_2(\mathbf{x})$ is quite limited, which plays a more obvious role than $f_1(\mathbf{x})$ and $f_3(\mathbf{x})$. And the point $C$ optimal solution was at the lowest area of the $f_1(\mathbf{x})$ , $f_2(\mathbf{x})$ and $f_3(\mathbf{x})$.

\subsection{3-D Cavitation Bubble Cluster Reconstruction}
\begin{figure}
  \centering

  \includegraphics[width=9cm]{05.jpg}\\
  \caption{Experimental images in a short time}\label{fig05}
\end{figure}

Figure \ref{fig05} shows three randomly selected frames of the experimental video, whose time interval was only about 23 milliseconds (ms). The cavitation bubbles inside the valve were captured from the three sides.

An image processing algorithm called the frame differencing method was applied to detect the features of the cavitation bubbles. All the two dimensional (2D) bubble features of the relative motion compared to the previous near frame were extracted. The 3D bubble reconstruction in this paper was based on space rectangular coordinate system. The spatial coordinates of the cavitation bubbles in the valve was provided by the position information of the experiment images from the three directions of left (L), right (R), back (B). The bubble position coordinates on the horizontal axis from the L and B sides' images were directly used as the $x$ coordinate values of the bubbles in the spatial location and the R side's image provided the $y$ coordinate values. After matching the 2D bubble features, the 3D cavitation bubble cluster was reconstructed as shown in Figure \ref{fig06}. From the reconstruction results, the change process of the generation and collapse of the cavitation bubbles can be analyzed. And the number and motion rack of the bubbles can be further calculated.

\begin{figure}
  \centering

  \includegraphics[width=12cm]{06.jpg}\\
  \caption{3-D reconstruction results of bubble flow in a short time}\label{fig06}
\end{figure}

\section{Conclusion}
In this paper, we proposed a novel 3D image capture method and applied an improved HS algorithm to optimize its design arrangement. At last, as a case study, this method was applied in a water hydraulic valve to capture and reconstruct the cavitation bubble cluster. By analyzing the position distribution and density of the Pareto solutions about a representative point, the advantage and improvement of the modified HS method was verified. Besides, the cavitation experiment was implemented. Through analysis and calculation of the experimental images, the 3D image of the cavitation bubbles was realized. The reconstruction results were quite accurate and effective. And the effectiveness of the 3D imaging device was testified. The 3D imaging method can be also applied in various multiphase flow measurements and has quite good flexibility and adaptability for different observed object.

\section*{Acknowledgment}
This work was supported by the Natural Science Foundation of China [grant number 51875113]; Natural Science Foundation of the Heilongjiang Province of China [grant number F2016003]; 'Jinshan Talent' Zhenjiang Manufacture 2025 Leading
 Talent Project; and 'Jiangyan Planning' Project in Yangzhong City.

\section*{References}

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text:
Resonance Raman spectroscopy
Resonance Raman spectroscopy (RR spectroscopy) is a Raman spectroscopy technique in which the incident photon energy is close in energy to an electronic transition of a compound or material under examination.[1] The frequency coincidence (or resonance) can lead to greatly enhanced intensity of the Raman scattering, which facilitates the study of chemical compounds present at low concentrations.[2]
Raman scattering is usually extremely weak, since only about 1 in 10 million photons that hit a sample are scattered with a loss (Stokes) or gain (anti-Stokes) in energy from changes in vibrational energy of the molecules in the sample; the rest of the photons are scattered with no change in energy. Resonance enhancement of Raman scattering requires the incident wavelength (usually from a laser) to be close to that of an electronic transition of the molecules. In larger molecules the change in electron density can be largely confined to one part of the molecule, a chromophore, and in these cases the Raman bands that are enhanced are primarily from those parts of the molecule in which the electronic transition leads to a change in bond length or force constant in the excited state of the chromophore. For large molecules such as proteins, this selectivity helps to identify the observed bands as originating from vibrational modes of specific parts of the molecule or protein, such as the heme unit within myoglobin.[3]
OverviewEdit
Raman spectroscopy and RR spectroscopy provide information about the vibrations of molecules, and can also be used for identifying unknown substances. RR spectroscopy has found wide application to the analysis of bioinorganic molecules. The technique measures the energy required to change the vibrational state of a molecule as does infrared (IR) spectroscopy. The mechanism and selection rules are different in each technique, however, band positions are identical and therefore the two methods provide complementary information.
Infrared spectroscopy involves measuring the direct absorption of photons with the appropriate energy to excite molecular bond vibrational modes and phonons. The wavelengths of these photons lie in the infrared region of the spectrum, hence the name of the technique. Raman spectroscopy measures the excitation of bond vibrations by an inelastic scattering process, in which the incident photons are more energetic (usually in the visible, ultraviolet or even X-ray region) and lose (or gain in the case of anti-Stokes Raman scattering) only part of their energy to the sample. The two methods are complementary because some vibrational transitions that are observed in IR spectroscopy are not observed in Raman spectroscopy, and vice versa. RR spectroscopy is an extension of conventional Raman spectroscopy that can provide increased sensitivity to specific (colored) compounds that are present at low concentrations (micro to millimolar) in an otherwise complex mixture of compounds.
An advantage of resonance Raman spectroscopy over (normal) Raman spectroscopy is that the intensity of bands can be increased by several orders of magnitude. An application that illustrates this advantage is the study of the dioxygen unit in cytochrome c oxidase. Identification of the band associated with the O–O stretching vibration was confirmed by using 18O–16O and 16O–16O isotopologues.[4]
Basic theoryEdit
Rayleigh scattering, Stokes Raman scattering, and anti-Stokes Raman scattering
The frequencies of molecular vibrations range from less than 1012 to approximately 1014 Hz. These frequencies correspond to radiation in the infrared (IR) region of the electromagnetic spectrum. At any given instant, each molecule in a sample has a certain amount of vibrational energy. However, the amount of vibrational energy that a molecule has continually changes due to collisions and other interactions with other molecules in the sample.
At room temperature, most molecules are in the lowest energy state—known as the ground state. A few molecules are in higher energy states—known as excited states. The fraction of molecules occupying a given vibrational mode at a given temperature can be calculated using the Boltzmann distribution. Performing such a calculation shows that, for relatively low temperatures (such as those used for most routine spectroscopy), most of the molecules occupy the ground vibrational state (except in the case of low-frequency modes). Such a molecule can be excited to a higher vibrational mode through the direct absorption of a photon of the appropriate energy. This is the mechanism by which IR spectroscopy operates: infrared radiation is passed through the sample, and the intensity of the transmitted light is compared with that of the incident light. A reduction in intensity at a given wavelength of light indicates the absorption of energy by a vibrational transition. The energy, E {\displaystyle E}
, of a photon is
E = h ν {\displaystyle E=h\nu }
where h {\displaystyle h}
is Planck's constant and ν {\displaystyle \nu }
is the frequency of the radiation. Thus, the energy required for such transition may be calculated if the frequency of the incident radiation is known.
It is also possible to observe molecular vibrations by an inelastic scattering process, Stokes Raman scattering being one such process. A photon is absorbed and then re-emitted (scattered) with lower energy. The difference in energy between the absorbed and re-emitted photons corresponds to the energy required to excite a molecule to a higher vibrational mode. Anti-Stokes Raman scattering is another inelastic scattering process and only occurs from molecules starting in excited vibrational states; it results in light scattered with higher energy. Light scattered elastically (no change in energy between the incoming photons and the re-emitted/scattered photons) is known as Rayleigh scattering.
Generally, the difference in energy is recorded as the difference in wavenumber ( Δ ν ¯ {\displaystyle \Delta {\bar {\nu }}}
) between the laser light and the scattered light which is known as the Raman shift. A Raman spectrum is generated by plotting the intensity of the scattered light versus Δ ν ¯ {\displaystyle \Delta {\bar {\nu }}}
Like infrared spectroscopy, Raman spectroscopy can be used to identify chemical compounds because the values of Δ ν ¯ {\displaystyle \Delta {\bar {\nu }}}
are indicative of different chemical species (their so-called chemical fingerprint). This is because the frequencies of vibrational transitions depend on the atomic masses and the bond strengths. Thus, armed with a database of spectra from known compounds, one can unambiguously identify many different known chemical compounds based on a Raman spectrum. The number of vibrational modes scales with the number of atoms in a molecule, which means that the Raman spectra from large molecules is complicated. For example, proteins typically contain thousands of atoms and therefore have thousands of vibrational modes. If these modes have similar energies ( Δ ν ¯ {\displaystyle \Delta {\bar {\nu }}}
), then the spectrum may be incredibly cluttered and complicated.
Not all vibrational transitions are Raman active, meaning that some vibrational transitions do not appear in the Raman spectrum. This is because of the spectroscopic selection rules for Raman spectra. In contrast to IR spectroscopy, where a transition can only be seen when that particular vibration causes a net change in dipole moment of the molecule, in Raman spectroscopy only transitions where the polarizability of the molecule changes along the vibrational coordinate can be observed. This is the fundamental difference in how IR and Raman spectroscopy access the vibrational transitions. In Raman spectroscopy, the incoming photon causes a momentary distortion of the electron distribution around a bond in a molecule, followed by re-emission of the radiation as the bond returns to its normal state. This causes temporary polarization of the bond and an induced dipole that disappears upon relaxation. In a molecule with a center of symmetry, a change in dipole is accomplished by loss of the center of symmetry, while a change in polarizability is compatible with preservation of the center of symmetry. Thus, in a centrosymmetric molecule, asymmetrical stretching and bending are IR active and Raman inactive, while symmetrical stretching and bending is Raman active and IR inactive. Hence, in a centrosymmetric molecule, IR and Raman spectroscopy are mutually exclusive. For molecules without a center of symmetry, each vibrational mode may be IR active, Raman active, both, or neither. Symmetrical stretches and bends, however, tend to be Raman active.
Theory of resonance Raman scatteringEdit
In resonance Raman spectroscopy, the wavelength of the incoming photons coincides with an electronic transition of the molecule or material. Electronic excitation of a molecule results in structural changes which are reflected in the enhancement of Raman scattering of certain vibrational modes. Vibrational modes that undergo a change in bond length and/or force constant during the electronic excitation can show a large increase in polarizability and hence Raman intensity. This is known as Tsuboi's rule, which gives a qualitative relationship between the nature of an electronic transition and the enhancement pattern in resonance Raman spectroscopy.[5] The enhancement factor can be by a factor of 10 to > 100,000 and is most apparent in the case of π-π* transitions and least for metal centered (d–d) transitions.[6]
There are two primary methods used to quantitatively understand resonance Raman enhancement. These are the transform theory, developed by Albrecht and the time-dependent theory developed by Heller.[7]
ApplicationsEdit
The selective enhancement of the Raman scattering from specific modes under resonance conditions means that resonance Raman spectroscopy is especially useful for large biomolecules with chromophores embedded in their structure. In such chromophores, the resonance scattering from charge-transfer (CT) electronic transitions of the metal complex generally result in enhancement of metal-ligand stretching modes, as well as some of the modes associated with the ligands alone. Hence, in a biomolecule such as hemoglobin, tuning the laser to near the charge-transfer electronic transition of the iron center results in a spectrum reflecting only the stretching and bending modes associated with the tetrapyrrole-iron group. Consequently, in a molecule with thousands of vibrational modes, RR spectroscopy allows us to look at relatively few vibrational modes at a time. The Raman spectrum of a protein containing perhaps hundreds of peptide bonds but only a single porphyrin molecule may show only the vibrations associated with the porphyrin. This reduces the complexity of the spectrum and allows for easier identification of an unknown protein. Also, if a protein has more than one chromophore, different chromophores can be studied individually if their CT bands differ in energy. In addition to identifying compounds, RR spectroscopy can also supply structural identification about chromophores in some cases.
The main advantage of RR spectroscopy over non-resonant Raman spectroscopy is the large increase in intensity of the bands in question (by as much as a factor of 106). This allows RR spectra to be obtained with sample concentrations as low as 10−8 M. It also makes it possible to record Raman spectra of short-lived excited state species when pulsed lasers are used.[8] This is in stark contrast to non-resonant Raman spectra, which usually requires concentrations greater than 0.01 M. RR spectra usually exhibit fewer bands than the non resonant Raman spectrum of a compound, and the enhancement seen for each band can vary depending on the electronic transitions with which the laser is resonant. Since typically, RR spectroscopy are obtained with lasers at visible and near-UV wavelengths, spectra are more likely to be affected by fluorescence. Furthermore, photodegradation (photobleaching) and heating of the sample can occur as the sample also absorbs the excitation light, dissipating the energy as heat.
InstrumentationEdit
Raman microscope
The instrumentation used for resonance Raman spectroscopy is identical to that used for Raman spectroscopy; specifically, a highly monochromatic light source (a laser), with an emission wavelength in either the near-infrared, visible, or near-ultraviolet region of the spectrum. Since the energy of electronic transitions (i.e. the color) varies widely from compound to compound, wavelength-tunable lasers, which appeared in the early 1970s, are useful as they can be tuned to coincide with an electronic transition (resonance). However, the broadness of electronic transitions means that many laser wavelengths may be necessary and multi-line lasers (Argon and Krypton ion) are commonly used. The essential point is that the wavelength of the laser emission is coincident with an electronic absorption band of the compound of interest. The spectra obtained contain non-resonant Raman scattering of the matrix (e.g., solvent) also.
Sample handling in Raman spectroscopy offers considerable advantages over FTIR spectroscopy in that glass can be used for windows, lenses, and other optical components. A further advantage is that whereas water absorbs strongly in the infrared region, which limits the pathlengths that can be used and masking large region of the spectrum, the intensity of Raman scattering from water is usually weak and direct absorption interferes only when near-infrared lasers (e.g., 1064 nm) are used. Therefore, water is an ideal solvent. However, since the laser is focused to a relatively small spot size, rapid heating of samples can occur. When resonance Raman spectra are recorded, however, sample heating and photo-bleaching can cause damage and a change to the Raman spectrum obtained. Furthermore, if the absorbance of the sample is high (> OD 2) over the wavelength range in which the Raman spectrum is recorded then inner-filter effects (reabsorption of the Raman scattering by the sample) can decrease signal intensity dramatically. Typically, the sample is placed into a tube, which can then be spun to decrease the sample's exposure to the laser light, and reduce the effects of photodegradation. Gaseous, liquid, and solid samples can all be analyzed using RR spectroscopy.
Although scattered light leaves the sample in all directions the collection of the scattered light is achieved only over a relatively small solid angle by a lens and directed to the spectrograph and CCD detector. The laser beam can be at any angle with respect to the optical axis used to collect Raman scattering. In free space systems, the laser path is typically at an angle of 180° or 135° (a so-called back scattering arrangement). The 180° arrangement is typically used in microscopes and fiber optic based Raman probes. Other arrangements involve the laser passing at 90° with respect to the optical axis. Detection angles of 90° and 0° are less frequently used.
The collected scattered radiation is focused into a spectrograph, in which the light is first collimated and then dispersed by a diffraction grating and refocused onto a CCD camera. The entire spectrum is recorded simultaneously and multiple scans can be acquired in a short period of time, which can increase the signal-to-noise ratio of the spectrum through averaging. Use of this (or equivalent) equipment and following an appropriate protocol[9] can yield better than 10% repeatability in absolute measurements for the rate of Raman scattering. This can be useful with resonance Raman for accurately determining optical transitions in structures with strong Van Hove singularities.[10]
Resonance hyper-Raman spectroscopyEdit
Resonance hyper-Raman spectroscopy is a variation on resonance Raman spectroscopy in which the aim is to achieve an excitation to a particular energy level in the target molecule of the sample by a phenomenon known as two-photon absorption. In two-photon absorption, two photons are simultaneously absorbed into a molecule. When that molecule relaxes from this excited state to its ground state, only one photon is emitted. This is a type of fluorescence.
In resonance Raman spectroscopy, certain parts of molecules can be targeted by adjusting the wavelength of the incident laser beam to the "color" (energy between two desired electron quantum levels) of the part of the molecule that is being studied. This is known as resonance fluorescence, hence the addition of the term "resonance" to the name "Raman spectroscopy". Some excited states can be achieved via single or double photon absorption. In these cases, however, the use of double photon excitation can be used to attain more information about these excited states than would a single photon absorption. There are some limitations and consequences to both resonance Raman and resonance hyper Raman spectroscopy.[11]
Both resonance Raman and resonance hyper Raman spectroscopy employ a tunable laser. The wavelength of a tunable laser can be adjusted by the operator to wavelengths within a particular range. This frequency range, however, is dependent on the laser's design. Regular resonance Raman spectroscopy, therefore, is only sensitive to the electron energy transitions that match that of the laser used in the experiment. The molecular parts that can be studied by normal resonance Raman spectroscopy is therefore limited to those bonds that happen to have a "color" that fits somewhere into the spectrum of "colors" to which the laser used in that particular device can be tuned. Resonance hyper Raman spectroscopy, on the other hand, can excite atoms to emit light at wavelengths outside the laser's tunable range, thus expanding the range of possible components of a molecule that can be excited and therefore studied.
Resonance hyper Raman spectroscopy is one of the types of "non-linear" Raman spectroscopy. In linear Raman spectroscopy, the amount of energy that goes into the excitation of an atom is the same amount that leaves the electron cloud of that atom when a photon is emitted and the electron cloud relaxes back down to its ground state. The term non-linear signifies reduced emission energy compared to input energy. In other words, the energy into the system no longer matches the energy out of the system. This is due to the fact that the energy input in hyper-Raman spectroscopy is much larger than that of typical Raman spectroscopy. Non-linear Raman spectroscopy tends to be more sensitive than conventional Raman spectroscopy. Additionally, it can significantly reduce, or even eliminate the effects of fluorescence.[12]
X-Ray Raman scatteringEdit
In the X-ray region, enough energy is available for making electronic transitions possible. At core level resonances, X-ray Raman scattering can become the dominating part of the X-ray fluorescence spectrum. This is due to the resonant behavior of the Kramers-Heisenberg formula in which the denominator is minimized for incident energies that equal a core level. This type of scattering is also known as Resonant inelastic X-ray scattering (RIXS). In the soft X-ray range, RIXS has been shown to reflect crystal field excitations, which are often hard to observe with any other technique. Application of RIXS to strongly correlated materials is of particular value for gaining knowledge about their electronic structure. For certain wide band materials such as graphite, RIXS has been shown to (nearly) conserve crystal momentum and thus has found use as a complementary bandmapping technique.
Tip-enhanced Raman spectroscopy
Vibronic spectroscopy
Depolarization ratio
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