The birth so rare you've probably never heard of it.

Jessica Antoniadis secretly hoped the birth of her second child, Peter would be an accidental home birth.

The 28-year-old mother from Sydney has two boys, one is almost two years old now and the other is three months old.

Determined to do things differently after a traumatic 58 hour birth the first time around, Jessica hired a doula and a birth photographer for the birth of second child, Peter.

“When I did go into labour at two o’clock in the morning I just was hanging out by myself in the dark just trying to move things along and about an hour later the contractions were really strong and I was freaking out a little bit because things were happening a lot faster than last time.

WATCH: Women share the one thing no one told them about giving birth. Post continues after video.

“So I got my husband up and called the doula and a few hours later we called Bel, the photographer. When they turned up every contraction was still one to two minutes long and no more than three mintues apart. It was just happening really quick.

“It was a bit weird having all these people in the room just all, you know, I was the centre of attention. That was a bit weird for me.

“I was like ‘oh, wouldn’t be great to have all these people supporting me’ but when it came down to it I was like, ‘oh… hi.’

Jessica, during her second stage of labour. Image courtesy The First Hello Project.

"I was walking around between contractions and I was like, 'Oh do you guys want tea? Do you want something to eat? Do you want the tv on? I don't know what I'm meant to do.'"

Jessica got to the hospital at about 11am and Peter was born four hours later. After her first birth, at 58 hours long Jessica says "this was a breeze".

But what makes Peter's birth story so special is that he was born en caul, a rare birth phenomenon where the baby is born inside his or her amniotic sac.

(As opposed to a straight caul birth, where a baby is born with a piece of membrane covering their head and face; a birth that is even rarer.)

About one in every 80,000 babies will be born en caul, so rare that many midwives and obstetricians will go their entire career without seeing one.

"We thought my waters had broken because I had a little bit of a trickle down my leg," Jessica tells me.

"But when he was crowning my midwife and doula were like, 'Whoa. Hold on. Hang on. He's still in the sac.' They were telling me, 'Don't push!' and I was saying, 'I'm not pushing. My body's just getting him out!' And they were saying, 'No, just hold him there.'"

"I'm not pushing. My body's just getting him out." Here, you can see Peter still inside the amniotic sac. Image courtesy The First Hello Project.

"So Bel came round and took some photos which was amazing. I'm so glad she was there."

Jessica didn't get to see Peter in the sac. "I wish I had." Her birth position on the floor meant that she couldn't get into the position to see him.

The midwife and the doula were all just really excited. "I was just focused on trying to stop my body from pushing him out."

Jessica is very grateful she had a birth photographer with her - it was the only way she got to see Peter in his amniotic sac.

Babies born in the sac are said to have life long good luck and to have a natural affinity with water; some myths hold that babies born en caul will never drown.

Wikipedia lists Liberace, Lord Byron and Sigmund Freud as famous caul babies. Caul babies also regularly feature in literature; David Copperfield, Oscar from Oscar and Lucinda and Quoyle's friend Partridge from The Shipping News among other characters were all born caul or en caul.

In medieval times, the caul was presented to the mother as a token of good luck. Jessica, it's safe to say, is just enjoying Bel Pangburn's photos of Peter en caul.

Jessica, looking back three months after Peter's birth is very positive.

"With my firstborn, I had every drug on offer and pushed away my husband. I wanted to do it alone and I ended up feeling alone throughout the whole labour.

"With my second (Peter), I chose my 'tribe' carefully and had never needed my husband as much as I did during those 14 hours.

"Between my doula, Bel (the photographer), my midwife and my husband, I knew this birth was going to be different. I felt so supported by everyone. I felt safe. And even though at times I said that I couldn't go on because I was exhausted, I pushed through and ended up with the birth I had always dreamed of - empowering, completely unmedicated and my son was born en caul. (And I didn't even tear until I delivered my placenta!)

"Also although I had always dreamed of having my labours photographed or filmed, hiring Bel & Riv [from The First Hello Project] was a huge step for me and was a way of accepting my image and to push me to finally coming out from behind the camera."

Jessica and I finish our conversation with me asking the question we all say you should never ask. 'Are you going to have more children?' Jessica laughs and says she sure is.

"It must have been a good birth if within a week of giving birth my husband had written down the next name he wanted to use and written down the date he wanted us to aim for. I said, 'but it's only been a week' and he said, 'yeah but we'll be fine!'"

The First Hello is a collaborative project sharing the realistic beauty of birth, between Sydney photographers Bel Pangburn and River Bennett. You can get more details at their website or follow their work on Instagram.