I made a pulse oximeter and instead of using Max 30100 I’m using 2 leds (1 red and 1 IR 940 nm sender) and one photodiode 940 nm receiver and I’m using Arduino pro mini (pin A1 is assigned to analog signal input from photodiode and pin 10 and 11 are connected to base of BC547 Transistors with two 4.7k ohm resistors) and O’LED 0.96 ssd 1306 for display( SDA and SCL are connected to A4 and A5 of arduino pro) my power supply is 9v DC battery with a LM7805 and also pins for IR and Red led are connected to two bases of BC547 with a 4.7 k Ohm resistors and also the collector pin is connected short leg of LED cathode and Emitter pin is connected to ground and anode of led are connected to 5 v dc and also photodiode is connected to A1 and through a junction is connected to Vcc with a 10 K resistor 
code :
#include <Wire.h> 
//#include <LiquidCrystal_I2C.h>
#include <SPI.h>

#include <Adafruit_GFX.h>
#include <Adafruit_SSD1306.h>

#define SCREEN_WIDTH 128 // OLED display width, in pixels
#define SCREEN_HEIGHT 32 // OLED display height, in pixels

// Declaration for an SSD1306 display connected to I2C (SDA, SCL pins)
#define OLED_RESET     4
Adafruit_SSD1306 display(SCREEN_WIDTH, SCREEN_HEIGHT, &Wire, OLED_RESET);


#define maxperiod_siz 80 // max number of samples in a period
#define measures 10      // number of periods stored
#define samp_siz 4       // number of samples for average
#define rise_threshold 3 // number of rising measures to determine a peak
 
// a liquid crystal displays BPM 
//LiquidCrystal_I2C lcd(0x3F, 16, 2);

int T = 20;              // slot milliseconds to read a value from the sensor
int sensorPin = A1; 
int REDLed = 10;
int IRLed = 11;

int SpO2;
int avBPM;

byte sym[3][8] = {
 {
  B00000,
  B01010,
  B11111,
  B11111,
  B01110,
  B00100,
  B00000,
  B00000
},{
  B00000,
  B00000,
  B00000,
  B11000,
  B00100,
  B01000,
  B10000,
  B11100
},{
  B00000,
  B00100,
  B01010,
  B00010,
  B00100,
  B00100,
  B00000,
  B00100
}
};

void setup() {
   Serial.begin(9600);
   Serial.flush();
   pinMode(sensorPin,INPUT);
   pinMode(REDLed,OUTPUT);
   pinMode(IRLed,OUTPUT);

   // initialize the LCD
  // lcd.init();
  // lcd.backlight();

   // turn off leds
   digitalWrite(REDLed,LOW);
   digitalWrite(IRLed,LOW);

 //  for(int i=0;i<8;i++) lcd.createChar(i, sym[i]);
 if(!display.begin(SSD1306_SWITCHCAPVCC, 0x3C)) { // Address 0x3C for 128x32
    Serial.println(F("SSD1306 allocation failed"));
    for(;;); // Don't proceed, loop forever
  


}}

void loop ()
{
  /*display.clearDisplay();
   display.setTextSize(1); // Draw 2X-scale text
  display.setTextColor(SSD1306_WHITE);
  display.setCursor(20, 10);
  display.println("Insert Fingure");
       
  display.display();  */
  bool finger_status = true;
  
  float readsIR[samp_siz], sumIR,lastIR, reader, start;
  float readsRED[samp_siz], sumRED,lastRED;


  int period, samples;
  period=0; samples=0;
  int samplesCounter = 0;
  float readsIRMM[maxperiod_siz],readsREDMM[maxperiod_siz];
  int ptrMM =0;
  for (int i = 0; i < maxperiod_siz; i++) { readsIRMM[i] = 0;readsREDMM[i]=0;}
  float IRmax=0;
  float IRmin=0;
  float REDmax=0;
  float REDmin=0;
  double R=0;

  float measuresR[measures];
  int measuresPeriods[measures];
  int m = 0;
  for (int i = 0; i < measures; i++) { measuresPeriods[i]=0; measuresR[i]=0; }
   
  int ptr;

  float beforeIR;

  bool rising;
  int rise_count;
  int n;
  long int last_beat;
  for (int i = 0; i < samp_siz; i++) { readsIR[i] = 0; readsRED[i]=0; }
  sumIR = 0; sumRED=0; 
  ptr = 0; 
    
 

  while(1)
  {
    
    //
    // turn on IR LED
    digitalWrite(REDLed,LOW);
    digitalWrite(IRLed,HIGH);
    
    // calculate an average of the sensor
    // during a 20 ms (T) period (this will eliminate
    // the 50 Hz noise caused by electric light
    n = 0;
    start = millis();
    reader = 0.;
    do
    {
      reader += analogRead (sensorPin);
      n++;
    }
    while (millis() < start + T);  
    reader /= n;  // we got an average
    // Add the newest measurement to an array
    // and subtract the oldest measurement from the array
    // to maintain a sum of last measurements
    sumIR -= readsIR[ptr];
    sumIR += reader;
    readsIR[ptr] = reader;
    lastIR = sumIR / samp_siz;

    
    
    

    //
    // TURN ON RED LED and do the same
    
    digitalWrite(REDLed,HIGH);
    digitalWrite(IRLed,LOW);

    n = 0;
    start = millis();
    reader = 0.;
    do
    {
      reader += analogRead (sensorPin);
      n++;
    }
    while (millis() < start + T);  
    reader /= n;  // we got an average
    // Add the newest measurement to an array
    // and subtract the oldest measurement from the array
    // to maintain a sum of last measurements
    sumRED -= readsRED[ptr];
    sumRED += reader;
    readsRED[ptr] = reader;
    lastRED = sumRED / samp_siz;







    //                                  
    // R CALCULATION
    // save all the samples of a period both for IR and for RED
    readsIRMM[ptrMM]=lastIR;
    readsREDMM[ptrMM]=lastRED;
    ptrMM++;
    ptrMM %= maxperiod_siz;
    samplesCounter++;
    //
    // if I've saved all the samples of a period, look to find
    // max and min values and calculate R parameter
    if(samplesCounter>=samples){
      samplesCounter =0;
      IRmax = 0; IRmin=1023; REDmax = 0; REDmin=1023;
      for(int i=0;i<maxperiod_siz;i++) {
        if( readsIRMM[i]> IRmax) IRmax = readsIRMM[i];
        if( readsIRMM[i]>0 && readsIRMM[i]< IRmin ) IRmin = readsIRMM[i];
        readsIRMM[i] =0;
        if( readsREDMM[i]> REDmax) REDmax = readsREDMM[i];
        if( readsREDMM[i]>0 && readsREDMM[i]< REDmin ) REDmin = readsREDMM[i];
        readsREDMM[i] =0;
      }
      R =  ( (REDmax-REDmin) / REDmin) / ( (IRmax-IRmin) / IRmin ) ;
    }

    

    




    // check that the finger is placed inside
    // the sensor. If the finger is missing 
    // RED curve is under the IR.
    //
    if (lastRED < lastIR) {
      if(finger_status==true) {
        finger_status = false;
       // lcd.clear();
       // lcd.setCursor(0,0);
       // lcd.print("No finger?"); 
        //Serial.println("No finger?");       
      }
    } else {
      if(finger_status==false) {
       // lcd.clear();
        finger_status = true;

            //lcd.setCursor(10,0);
            //lcd.print("c=");
 //Serial.println("c");
            //lcd.setCursor(0,0);
            //lcd.print("bpm");
           // lcd.setCursor(0,1);
           // lcd.print("SpO"); lcd.write(1);  //2            
           // lcd.setCursor(10,1);
          //  lcd.print("R=");

        
      }
    }


    float avR = 0;
    avBPM=0;

   

    if (finger_status==true){

      
     
       // lastIR holds the average of the values in the array
       // check for a rising curve (= a heart beat)
       if (lastIR > beforeIR)
       {
 
         rise_count++;  // count the number of samples that are rising
         if (!rising && rise_count > rise_threshold)
         {
          // lcd.setCursor(3,0); 
          // lcd.write( 0 );       // <3
            // Ok, we have detected a rising curve, which implies a heartbeat.
            // Record the time since last beat, keep track of the 10 previous
            // peaks to get an average value.
            // The rising flag prevents us from detecting the same rise 
            // more than once. 
            rising = true;

            measuresR[m] = R;
            measuresPeriods[m] = millis() - last_beat;
            last_beat = millis();
            int period = 0;
            for(int i =0; i<measures; i++) period += measuresPeriods[i];

            // calculate average period and number of samples
            // to store to find min and max values
            period = period / measures;
            samples = period / (2*T);
              
             int avPeriod = 0;

            int c = 0;
            // c stores the number of good measures (not floating more than 10%),
            // in the last 10 peaks
            for(int i =1; i<measures; i++) {
              if ( (measuresPeriods[i] <  measuresPeriods[i-1] * 1.1)  &&  
                    (measuresPeriods[i] >  measuresPeriods[i-1] / 1.1)  ) {

                  c++;
                  avPeriod += measuresPeriods[i];
                  avR += measuresR[i];

              }
            }
              
            m++;
            m %= measures;
                        
           // lcd.setCursor(12,0);
           // lcd.print(String(c)+"  ");
 //Serial.println(String(c)+"  ");
            // bpm and R shown are calculated as the
            // average of at least 5 good peaks
            avBPM = 60000 / ( avPeriod / c) ;
            avR = avR / c ;

            // if there are at last 5 measures 
            //lcd.setCursor(12,1);
            if(c==0) /*lcd.print("    ");*/ Serial.println("  ");
            else /*lcd.print(String(avR) + " ");*/ Serial.println(" ");
            
            // if there are at least 5 good measures...
            if(c > 4) {

              //
              // SATURTION IS A FUNCTION OF R (calibration)
              // Y = k*x + m
              // k and m are calculated with another oximeter
               SpO2 = -19 * R + 99;
              
              //lcd.setCursor(4,0);
              if(avBPM > 40 && avBPM <220) Serial.println(String(avBPM)+" ");
              dis();
            //lcd.print(String(avBPM)+" "); //else lcd.print("---");

              //lcd.setCursor(4,1); 
              if(SpO2 > 70 && SpO2 <110) Serial.println( " " + String(SpO2) +"% "); //lcd.print( " " + String(SpO2) +"% "); //else lcd.print("--% ");
                   dis();             

            } else {
              if(c <3) {
               display.clearDisplay();
                  display.setTextSize(1); // Draw 2X-scale text
                  display.setTextColor(SSD1306_WHITE);
                  display.setCursor(20, 10);
                  display.println("Insert Fingure");
                  //display.setTextSize(1); // Draw 2X-scale text
       
                  display.display();  
                // if less then 2 measures add ?
                //lcd.setCursor(3,0); lcd.write( 2 ); //bpm ?
                //lcd.setCursor(4,1); lcd.write( 2 ); //SpO2 ?
              }
            }
   
           
         }
       }
       else
       {
         // Ok, the curve is falling
         rising = false;
         rise_count = 0;
         //lcd.setCursor(3,0);lcd.print(" ");
       }
  
       // to compare it with the new value and find peaks
       beforeIR = lastIR;
  

   } // finger is inside 




    
    // PLOT everything
   //Serial.print(lastIR);
    Serial.print(",");
   // Serial.print(lastRED);
    /*
     * Serial.print(",");
    Serial.print(R);    
    Serial.print(",");   
    Serial.print(IRmax);
    Serial.print(",");
    Serial.print(IRmin);
    Serial.print(",");
    Serial.print(REDmax);
    Serial.print(",");
    Serial.print(REDmin);
    Serial.print(",");
    Serial.print(avR);
    Serial.print(",");
    Serial.print(avBPM); */
    Serial.println();



   // handle the arrays      
   ptr++;
   ptr %= samp_siz;
  
     
  } // loop while 1
}

void dis()
{
  display.clearDisplay();
  display.setTextSize(1); // Draw 2X-scale text
  display.setTextColor(SSD1306_WHITE);
  display.setCursor(10, 0);
  display.println("SpO2%");
  display.setCursor(90, 0);
  display.println("BpM");
   display.setTextSize(2);
   display.setCursor(10, 11);
   display.print(SpO2);
   display.println("%");
  display.setCursor(80, 11);
  display.println(avBPM);
  display.display();      // Show initial text
  
 // delay(100);
 }

give me a full explanation of algorithms , function, calculations with their codes