作为一个光学专业的学生，光的干涉是一个基础知识点。所以尝试着做了个安卓app，来模拟球面波的干涉现象，效果如下：

通过改变参数，可以观察到不同的现象。

先从介绍干涉实验原理开始，首先如下图所示：

点光源s1和s2在同一直线上，设为x轴，观察屏在距离它们为D的位置上，观察屏平行于y-z平面，在观察屏上各点光强不同，即存在干涉现象。s1和s2发射球面波，所以在空间任意一点上的光强与距离的平方成反比，而干涉理论公式为：I = I1+I2+sqrt(I1*I2)*cos(phi)。

下面是app的具体实现，下面给出定义的各变量的含义：

 private double length=5;//观察范围半宽度5mm
    private double width=0.2;//两点间距0.2mm
    private double D = 30;//点光源所在平面到观察屏距离30mm
    private double wavelength = 600;//波长600nm
    private double k;//波矢量
    private double dlength;//观察屏刻度
//    private double dwidth;
    int ny = 151;//观察屏范围分割数
    private double I[][];//记录观察屏上的点的强度

    private EditText rectLength;//设置观察范围
    private EditText pointWidth;//设置点间距
    private EditText editTextWavelength;//设置波长
    private Button buttonSet;

然后自定义View类用于绘制干涉现象，通过选定屏幕一个区域，将区域分割成一个个的点，作为采样点，在采样点上画小圆点，根据采样点的光强大小，设置颜色深浅以表示光强大小：

 @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        canvas.drawColor(Color.BLACK);
        if (I==null){
            I = new double[151][151];
        }
        drawPoint(canvas,I);
    }

    private void drawPoint(Canvas canvas,double I[][]){
        for (int i = 0; i < I.length; i++) {
            for (int j = 0; j < I.length; j++) {
                paint = new Paint();
                paint.setARGB(255,0,0, (int) I[i][j]);//改变颜色大小，仅改变蓝色
                canvas.drawCircle(startX+i*deltaX,startY+j*deltaY,8,paint);
            }

        }

    }

还需要定义一个方法，使得在MainActivity中获得光强值后能更新数值：

public void setI(double I[][]){
        if (I!=null){
            this.I = I;
        }
    }

这样，我们就可以在MainActivity中根据参数设置进行计算并显示了。由于数值计算过程可能会比较久，因此，自定义一个新线程进行光强值计算：

class DataThread extends Thread{//自定义线程，用于计算观察范围内各点强度
        public Handler handler;
        @Override
        public void run() {
            Looper.prepare();
            handler = new Handler(){
                @Override
                public void handleMessage(Message msg) {
                    if (msg.what==0x123){
                        k = 2*Math.PI/wavelength*1000000;//k的单位是mm-1
                        I = new double[ny][ny];
                        dlength = 2*length/ny;//将观察范围分割

                        double Imax = 0;//强度最大值
                        double Imin = 255;//强度最小值
                        double l1,l2,phi;

                        for (int i = 0; i <ny ; i++) {
                            for (int j = 0; j <ny ; j++) {
                                //l1是右边的点光源到观察屏上各采样点的距离
                                l1 = Math.sqrt((-length+dlength*j)*(-length+dlength*j)+
                                        (-length+dlength*i)*(-length+dlength*i)+(D-width/2)*(D-width/2));
                                //l2是左边的点光源到观察屏上各采样点的距离
                                l2 = Math.sqrt((-length+dlength*j)*(-length+dlength*j)+
                                        (-length+dlength*i)*(-length+dlength*i)+(D+width/2)*(D+width/2));
                                phi = k*(l2-l1);//相位差
                                I[i][j] = (1/l1)*(1/l1)+(1/l2)*(1/l2)+2*(1/l1)*(1/l2)*Math.cos(phi);/*
                                设点光源振幅为1，球面波到空间某点出的光强与距离的平方成反比
                                即左边点光源光强：I1 = 1/l2^2，右边点光源光强：I2 = 1/l1^2
                                干涉公式：I = I1+I2+sqrt(I1*I2)*cos(phi)
                                */
                                if(I[i][j]>Imax)
                                    Imax = I[i][j];//取得最大值
                                if (I[i][j]<Imin)
                                    Imin = I[i][j];//取得最小值
                            }
                        }

                        for (int i=0;i<ny;i++){
                            for (int j = 0; j < ny; j++) {
                                I[i][j] = (I[i][j]-Imin)/(Imax-Imin)*255;//将强度大小等比放大到0~255范围，好设置颜色深浅
                            }
                        }
                        imaging.setI(I);
                        imaging.postInvalidate();
                    }
                }
            };
            Looper.loop();
        }
    }

当我们点击设定按钮时，更新参数值，并且发送消息：

buttonSet.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
                String s1 = rectLength.getText().toString();
                String s2 = pointWidth.getText().toString();
                String s3 = editTextWavelength.getText().toString();
                //输入不为空就更新相应的数值
                if (s1!=null&&!s1.equals("")){
                    length = Double.parseDouble(s1);
                }
                if (s2!=null&&!s2.equals("")){
                    width = Double.parseDouble(s2);
                }
                if (s3!=null&&!s3.equals("")){
                    wavelength = Double.parseDouble(s3);
                }
                Message msg = new Message();
                msg.what = 0x123;
                dataThread.handler.sendMessage(msg);
            }
        });

改变参数，效果如下：

           

附上完整代码：

public class MainActivity extends AppCompatActivity {
    private double length=5;//观察范围半宽度5mm
    private double width=0.2;//两点间距0.2mm
    private double D = 30;//点光源所在平面到观察屏距离30mm
    private double wavelength = 600;//波长600nm
    private double k;//波矢量
    private double dlength;//观察屏刻度
//    private double dwidth;
    int ny = 151;//观察屏范围分割数
    private double I[][];//记录观察屏上的点的强度

    private EditText rectLength;//设置观察范围
    private EditText pointWidth;//设置点间距
    private EditText editTextWavelength;//设置波长
    private Button buttonSet;
    private Imaging imaging;
    DataThread dataThread;

    class DataThread extends Thread{//自定义线程，用于计算观察范围内各点强度
        public Handler handler;
        @Override
        public void run() {
            Looper.prepare();
            handler = new Handler(){
                @Override
                public void handleMessage(Message msg) {
                    if (msg.what==0x123){
                        k = 2*Math.PI/wavelength*1000000;//k的单位是mm-1
                        I = new double[ny][ny];
                        dlength = 2*length/ny;//将观察范围分割

                        double Imax = 0;//强度最大值
                        double Imin = 255;//强度最小值
                        double l1,l2,phi;

                        for (int i = 0; i <ny ; i++) {
                            for (int j = 0; j <ny ; j++) {
                                //l1是右边的点光源到观察屏上各采样点的距离
                                l1 = Math.sqrt((-length+dlength*j)*(-length+dlength*j)+
                                        (-length+dlength*i)*(-length+dlength*i)+(D-width/2)*(D-width/2));
                                //l2是左边的点光源到观察屏上各采样点的距离
                                l2 = Math.sqrt((-length+dlength*j)*(-length+dlength*j)+
                                        (-length+dlength*i)*(-length+dlength*i)+(D+width/2)*(D+width/2));
                                phi = k*(l2-l1);//相位差
                                I[i][j] = (1/l1)*(1/l1)+(1/l2)*(1/l2)+2*(1/l1)*(1/l2)*Math.cos(phi);/*
                                设点光源振幅为1，球面波到空间某点出的光强与距离的平方成反比
                                即左边点光源光强：I1 = 1/l2^2，右边点光源光强：I2 = 1/l1^2
                                干涉公式：I = I1+I2+sqrt(I1*I2)*cos(phi)
                                */
                                if(I[i][j]>Imax)
                                    Imax = I[i][j];//取得最大值
                                if (I[i][j]<Imin)
                                    Imin = I[i][j];//取得最小值
                            }
                        }

                        for (int i=0;i<ny;i++){
                            for (int j = 0; j < ny; j++) {
                                I[i][j] = (I[i][j]-Imin)/(Imax-Imin)*255;//将强度大小等比放大到0~255范围，好设置颜色深浅
                            }
                        }
                        imaging.setI(I);
                        imaging.postInvalidate();
                    }
                }
            };
            Looper.loop();
        }
    }

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        rectLength = (EditText) findViewById(R.id.rect_len);
        pointWidth = (EditText) findViewById(R.id.rect_wid);
        editTextWavelength = (EditText) findViewById(R.id.wavelength);
        buttonSet = (Button) findViewById(R.id.bt_set);
        imaging = (Imaging) findViewById(R.id.show_image);
        dataThread = new DataThread();
        dataThread.start();//线程开启

        buttonSet.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
                String s1 = rectLength.getText().toString();
                String s2 = pointWidth.getText().toString();
                String s3 = editTextWavelength.getText().toString();
                //输入不为空就更新相应的数值
                if (s1!=null&&!s1.equals("")){
                    length = Double.parseDouble(s1);
                }
                if (s2!=null&&!s2.equals("")){
                    width = Double.parseDouble(s2);
                }
                if (s3!=null&&!s3.equals("")){
                    wavelength = Double.parseDouble(s3);
                }
                Message msg = new Message();
                msg.what = 0x123;
                dataThread.handler.sendMessage(msg);
            }
        });
    }
}

Imaging.java:

public class Imaging extends View{
    private float startX;//X轴起点
    private float startY;//Y轴起点
    private float deltaX;//采样点间距
    private float deltaY;
    private Paint paint;

    private double I[][];
    private int ny=151;

    public Imaging(Context context, AttributeSet attrs) {
        super(context, attrs);
    }

    @Override
    protected void onSizeChanged(int w, int h, int oldw, int oldh) {
        super.onSizeChanged(w, h, oldw, oldh);
        startX = (w-h)/2;//设置X轴起点
        startY = 0;//设置Y轴起点
        deltaX = deltaY = h/150;
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        canvas.drawColor(Color.BLACK);
        if (I==null){
            I = new double[151][151];
        }
        drawPoint(canvas,I);
    }

    private void drawPoint(Canvas canvas,double I[][]){
        for (int i = 0; i < I.length; i++) {
            for (int j = 0; j < I.length; j++) {
                paint = new Paint();
                paint.setARGB(255,0,0, (int) I[i][j]);//改变颜色大小，仅改变蓝色
                canvas.drawCircle(startX+i*deltaX,startY+j*deltaY,8,paint);
            }

        }

    }

    public void setI(double I[][]){
        if (I!=null){
            this.I = I;
        }
    }
}